Download math 92 winter 2014 take-it-homes

Math 92
Winter 2014
Homework
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Module 4, Lesson 1
Name___________________________________________
Directions: Do the following calculations. Show all the steps. Do not just use the exponent key on the
calculator.
Example: 5-2
Solution: 1/52 = 1/25 = 0.04
Answer: 0.04
1. 53
2. 62
3. 4-1
4. 3-2
5. 8-3
Directions: Use your calculator (using the exponent button) to calculate the following:
6. (4.3)3
7. (1.098)6
8. (3.5)-2
9. (4.1)-3
Directions: Use the short-cut to calculate the following. DO NOT use your calculator
10. 104
11. 1011
12. 109
13. 102
14. 10-4
15. 10-6
3
16. 10-1
17. 10-10
Directions: calculate the following using order of operations
18. 7 + 23
19. 9 - 22
20. 5 + 3∙52
21. (4+1)2 + 9∙33
22. 62 - 24
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Module 4, Lesson 2
Name___________________________________________
Directions: Convert the following numbers to scientific notation:
1. 43,000,000
2. 502,000,000
3. 2,901,900,000
4. 5,900
5. 423,000
6. 290,000
7. 0.000023
8. 0.000000607
9. 0.00000005087
10. 0.0000000609
Convert the following numbers to standard notation:
11. 2×103
12. 6.04×107
13. 3.33×105
14. 1.02×109
15. 6.2×106
16. 2.85×1013
17. 6.75×10-5
18. 3.2×10-8
19. 2.03x10-6
20. 8.003x10-4
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Do the following calculations with your calculator. For the numbers that have too many digits for the
calculator, enter the numbers using scientific notation button. Write the answers in both scientific
notation and in standard notation
21. 45,000,000 x 902,000,000
22. 205,900,000 x 6,200,000
23. 2,000,000 ÷ 0.0000024
24. 63,000,000 ÷ 0.052
25. (2×103)(3×102)
26. (2×105)(3×103)
27. (1.2×106) ÷ (4×102)
28. (1.05×104) ÷ (2.54×10-2)
29. (1.25×10-4) ÷ (5×102)
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Module 4, Lesson 3
Name___________________________________________
Directions: For each set of data, use Excel to make a scatterplot. Then decide if the data should be
modeled by a linear equation or a non-linear equation
1)
x
0
1
2
3
4
5
6
7
Y
18
24
27
25
35
50
80
125
2)
x
67
22
35
18
76
56
40
66
38
80
28
65
33
55
Y
142
45
75
32
146
110
82
132
74
158
55
132
68
112
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3) Explain why the scatterplot below is NOT linear. Include information about the residuals in your
explanation.
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Module 4, Lesson 4
Name___________________________________________
1. Give the order of each polynomial
a) 4x2 – 3x
b) 9.603x5 + 9.7x4 – 0.92x2 + 5.69
2. State how many terms are in each polynomial
a) 4x2 – 3x
b) 9.603x5 + 9.7x4 – 0.92x2 + 5.69
3. Graph the following polynomials (let x start at -3 and end at 3)
a) y = x2 + x – 2
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b) y = x2 – 9
c) y = x3 + x2 – 2x
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Module 4, Lesson 5
Name___________________________________________
Rainfall is important for plants to grow. In
years where there is a draught plants do
not grow very well, they are parched and
shrivel up. In years when there is flooding
the crops can get ruined by oversaturation
or flooding. A farmer in Skagit County
recorded the rainfall at his pumpkin farm
and the tons of pumpkins that were
produced over ten years, the data is
recorded below.
Rainfall (inches)
Yield (tons)
22.1
6354
20.9
5246
19.2
4922
12.4
4315
31.2
6011
34.6
5812
34.5
4911
16.0
4805
28.2
6066
33.2
4822
1) Which is the explanatory and response variable for this data set.
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2) Create a scatterplot for the data above (on a separate sheet of graph paper). Would a linear model
be appropriate for this data set?
3) Using Excel, create a 2nd order (quadratic) model for this data set, write the equation for the model.
4) Use the model to predict how many tons of pumpkins the Skagit County farmer will produce if the
annual rainfall is 25 inches.
Otoliths (earstones) are found in the heads of
fish. They are used by the fish to help the
fish with balance and movement through the
water. Otoliths are similar to tree rings in
that every year they add a visible layer.
Scientists use Otoliths to determine the age
of fish. Below is some data from a scientist
who determined the age and length of some
fish he collected.
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Age (years)
Length (inches)
1
4.9
2
8.7
2
8.3
3
7.7
4
11.7
5
14.2
6
14.1
6
15.7
7
15.9
8
17.9
9
18.4
9
17.3
10
19.0
10
19.6
11
18.7
12
22.1
12
21.5
13
26.7
14
25.3
1) Which is the explanatory and response variable?
2) Create a scatterplot for the data (on a separate sheet of paper). Is a linear model appropriate?
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3) Create a quadratic regression (degree 2) for the data. Is the quadratic regression appropriate? Write
down the equation for the quadratic model.
4) Create a cubic regression (order 3) for the data. Is the cubic regression appropriate? Write down the
equation for the cubic model.
5) Using the cubic model predict the length of a fish who is 8 years old.
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The Paris gun was the largest artillery piece
used in World War I. It was used by the
Germans to attack Paris from a distance of
over 80 miles. The distance of the fired
artillery is so great that those firing it must
consider the Coriolis Effect (the rotation of
the Earth) when firing it. Below is some
hypothetical data relating the altitude of an
artillery shell and the time it has been in the
air since firing.
Time (seconds)
Altitude (km)
25
18
50
32
75
39
100
40
125
33
150
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a) Identify which is the explanatory and response variables.
b) Create a scatterplot for this data (on a separate sheet of paper). Is a linear model appropriate?
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c) Create a quadratic model (degree 2) for this data, write down the equation for the quadratic model.
d) Estimate the height of an artillery shell 90 seconds after firing.
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Module 4, Lesson 6
Name___________________________________________
On “day zero”, a person is infected with a virus. He then spreads it to another person, so on “day
1”, two people are infected. The virus continues to spread, and the number of people infected
doubles each day.
1) Make a table showing the number of infected people from day 0 to day 8.
2) Predict how many people will be infected on day 20
3) Write a formula for the number of infected people on “day x”
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Module 4, Lesson 7
Name___________________________________________
1.
Joe’s monthly rent is $1,200. His landlord recently told him that his rent will increase by 4%.
What will be his new rent?
2.
bill?
Hillary’s monthly phone bill is $45.00, but it will increase by 6%. What will be her new phone
3.
A new pair of shoes cost $45.99, and there is a 9.2% tax. What is the final price?
4.
A new computer costs $850.00. After a 8.9% sales tax, what is the new price?
5.
The population of a city is 535,000 people, and is expected to grow by 5% over the next 10
years. What will be the new population?
6.
The population of a city is 720,000 people, and is expected to grow by 8% over the next 10
years. What will be the new population?
7.
Mary just bought a car for $15,000. The value will decrease by 10% over the next 2 years. What
will be the value of the car after two years?
8.
A new computer costs $900, and the value will decrease by 45% over the next 3 years. What will
be the value of the computer after 3 years?
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Directions: Make a compound interest table for the following investments
9. $4000, at 2% interest per year, for 4 years
10. $2,500, at 2.5% interest per year, for 5 years
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Module 4, Lesson 8
1
Name___________________________________________
The scatterplots below show radiation levels over time for Area 4, another testing site in Nevada.
One scatterplot is fit with a linear model and the other is fit with an exponential model. The
equations of the models are given below each scatterplot. In both equations, x represents the
number of years since 1985. Use the graphs and equations below to answer the following questions.
2000
2000
1800
1800
1600
1600
Radiation (mR/yr)
Radiation (mR/yr)
Area 4 Radiation Levels (mR/year)
1400
1200
1000
800
600
1400
1200
1000
800
600
Years
400
400
Years
200
0
5
10
15
20
25
200
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Least Squares Line: yˆ  43 x  1404
A
0
5
10
20
25
Exponential Model: yˆ  1680(0.94)
Complete the table below using the equation of the least squares regression line:
Year
x
Predicted Radiation Level
(in mR/year)
1985
1990
2005
2010
B
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Complete the table below using the equation of the exponential model:
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x
Year
x
Predicted Radiation Level
(in mR/year)
1985
1990
2005
2010
2
C
Explain the meaning of 1404 and -43 in the least squares line. In your explanation think about
the predicted radiation level.
D
Explain the meaning of 1680 and 0.94 in the exponential model. In your explanation think
about the predicted radiation level.
E
Does the exponential model show exponential growth or exponential decay? Explain how you
chose your answer.
F
If you consider a level of 1,000 mR/year safe, for what year does the linear model and
exponential model predict that Area 4 was safe?
G
If you consider a level of 440 mR/year safe, for what year does the linear model and
exponential model predict that Area 4 was safe?
Some oral medications help us get better by entering our bloodstream. After we take the medicine,
the amount of the medicine that is in our bloodstream will decreases over time. We can model this
decrease by an exponential curve. The following table shows the amount of acetaminophen (Tylenol
is the common name) in a person’s bloodstream t hours after a person takes the medicine. Use the
table and graph below to answer the following questions.
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Time
(in hours)
Amount of
Acetaminophen
(in mg)
0
650
1
305
2
100
3
65
4
28
5
12
A
The exponential model yˆ  650(0.46) x predicts the amount of acetaminophen in a person’s
bloodstream x hours after taking the drug. What is the initial amount of acetaminophen (the
amount of medicine that the person first took) in the person’s bloodstream?
B
When will the amount of acetaminophen be below 100 mg?
C
The exponential curve yˆ  650(0.46) x predicts the amount of acetaminophen in a person’s
bloodstream x hours after taking the drug. Use this equation to predict the amount of
acetaminophen in a person’s bloodstream 3.5 hours after he first took the medicine.
D
What is the value of b in the exponential curve? Does this indicate exponential growth or
exponential decay?
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Module 4, Lesson 9
Name___________________________________________
Directions: For each situation, compute the absolute increase or decrease, then calculate the
percentage decrease or increase:
1. a car’s speed increased from 40 mph to 50 mph
2. cost of a refrigerator went from $590 to $845
3. a town’s population decreased from 8000 people to 7500 people
4. The price of a computer decreased from $450 to $390
5. tuition increased from $4000 per quarter to $4900 per quarter
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Module 4, Lesson 10
1
2
Name___________________________________________
In this problem, you will be using an exponential model to think about the population changes in the
country of Madagascar where 𝑦̂ refers to the number of people (in millions) in Madagascar and 𝑥
refers to the number of years since 2000. You will be using the exponential model
yˆ  16.4(1.027) x to approximate your answers.
A
Use the model to determine the approximate population of Madagascar in 2000. Explain how
you used the model to determine the answer.
B
Is the population of Madagascar growing or decaying? Explain.
C
What is the percent increase or percent decrease of population of Madagascar each year?
D
What is the predicted population of Madagascar in 2015 and 2040? Round your answer to two
decimal places.
The quantity of ibuprofen 𝑦̂ (in mg) remaining in a person’s blood ℎ hours after taking the
medication can be approximated by the exponential model
yˆ  800(0.68) x
A
How much ibuprofen was initially taken? Explain.
B
Is the quantity of ibuprofen in the bloodstream growing or decaying over time? Explain.
C
What is the percent increase or percent decrease of ibuprofen each hour?
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D
What is the predicted amount of ibuprofen remaining in a person’s blood 3 hours after taking
the medicine? Round your answer to two decimal places.
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A
Identify which of the following models are examples of exponential growth. How do you know?
Explain your answer.
Model A: yˆ  589(0.99) x
Model B: yˆ  1025(1.11) x
Model C: yˆ  200(1.18) x
B
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List the models in order from the fastest rate of growth to the slowest rate of growth.
A Identify which of the following models are examples of exponential decay. How do you know?
Explain your answer.
Model A: yˆ  250(0.97) x
Model B: yˆ  526(1.02) x
Model C: yˆ  113(0.84) x
B List the models in order from the fastest rate of decay to the slowest rate of growth.
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Module 4, Lesson 11
Name___________________________________________
1) Evaluate the following without the use of a calculator:
a) 𝑙𝑜𝑔(100)
b) 𝑙𝑜𝑔(1000)
c) 𝑙𝑜𝑔(0.0001)
d) 𝑙𝑜𝑔(1E7)
e) 𝑙𝑜𝑔(−1000)
2) Determine if the statement is true or false without the use of a calculator.
a) 𝑙𝑜𝑔(50) > 2
True
False
b) 𝑙𝑜𝑔(0.02) > −2
True
False
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c) 𝑙𝑜𝑔(4.2𝐸 − 5) < −5
True
False
d) 𝑙𝑜𝑔(1) < 1
True
False
3) Evaluate the following using your calculator.
a) 𝑙𝑜𝑔(0.5)
b) 𝑙𝑜𝑔(50)
c) 𝑙𝑜𝑔(500)
d) 𝑙𝑜𝑔(5000)
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Module 4, Lesson 12
Name___________________________________________
Oil production has increased exponentially from 1890 to 1980. Below is the data. The explanatory
variable is the year, and the response variable is oil production, in millions of barrels of oil (Mbbl)
Reference: Moore, David S., and George P. McCabe (1989). Introduction to the Practice of Statistics.
Original source: Energy Information Administraton, recorded in Romer, Robert H., Energy: An
Introduction to Physics, W.H. Freeman, San Francisco, 1976 for 1880 to 1972, and in The World Almanac
and Book of Facts 1986 for more recent years.
Year
Mbbl
1880 30
1890 77
1900 149
1910 328
1920 689
1930 1412
1940 2150
1950 3803
1960 7674
1970 16690
1980 21732
Find an exponential model for this data. Let x = the year and let y = the oil production. Take the log of
each y, then use Excel to find the least-squares regression line, then convert to an exponential equation.
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Module 4, Lesson 13
Name___________________________________________
Directions: For each situation, decide if a linear or exponential model is best. You do not need to find the
equation.
1. y = the amount of a drug in a person’s bloodstream. X = hours. Each hour, the body removes 20 mg of
the drug.
2. y = the amount of a drug in a person’s bloodstream. X = hours. Each hour, the body removes 15% of
the drug.
3. An investment grows at 4% (compound interest) per year.
4. The number of people who are infected by a virus doubles every week.
5. The cost of a movie ticket increases by 50 cents every year.
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6. For each scatterplot, decide if a linear, polynomial, or exponential model would be the best fit. Give a
reason for your answer
7. Write a paragraph explaining the differences between linear and exponential models.
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Module 4, Review
Name___________________________________________
1) For each of the following, write E.G. (for exponential growth), ED (for exponential decay) L (for
linear), or P (for polynomial)
a) y = 80(1.5)x
b) y = 80 + 4x
c) y = 2x
d) y = 100 – 1.04x
e) y = (0.7)x
f) y = 56.89(0.93)x
g)
y
x
h)
y
x
i)
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y
x
j) The amount of money in the bank grows by 2.5% each year
k) The amount of money in the bank grows by $50 each year
l) The amount of money in the bank decreases by 20% each year
m) The amount of money in the bank decreases by $30 each year
2) In an exponential model, y = A Bx, explain how “A” affects the graph, and explain how “B” affects the
graph. Give some examples in your explanation
3) If the population of a city is 20,000 people, and is doubling every 20 years, what is the population 80
years from now?
4) Explain the differences between a linear equation and an exponential equation.
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5) Suppose, in the year 2000, there were 20 million music CDs sold in the U.S., and the number of music
CDs sold decreases at a rate of 5% each year.
a) Write an equation for the number of music CDs sold, x years after 2000.
b) Use the equation from part (a) to predict the number of music CDs that will be sold in the year 2015.
6) Sam earned $18 per hour and just got a 5% raise. What is his wage now?
7) A bag of potato chips normally cost $3.50, but now it’s for sale at a 15% discount. What is the new
price?
8) Last year, the population of a city was 525,000. Now the population is 560,000. What is the percent
increase?
9) Use your calculator to compute the following logarithms. Then explain what the answer means
a) log (980)
b) log(4300)
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c) log (0.09)
10) Calculate the following without a calculator, then explain what the answer means:
a) log (10,000)
b) log (100)
Answers to Module 4 Review Questions
1a) EG b) L c) EG d) L e) ED f) ED g) EG h) ED i) P j) EG k) L l) ED
m) L
2) A is the starting point, value when x = 0, and the y-intercept. B is the growth factor (if B> 1) or decay
factor (if B < 1).
3) 320,000 people
4) linear is straight, has a constant rate of change, and has the formula y = a + bx. Exponential is curved,
increases or decreases by a percentage, and has the formula y = abx.
5a) y = 20(0.95)x b) 9.27 million
6) $18.90
7) $2.98
8) 6.7%
9a) 2.99, which means 102.99 = 980 b) 3.63, which means 103.63 = 4300 c) -1.05, which means 10-1.05 =
0.09
10a) 4, which means 104 = 10,000 b) 2, which means 102 = 100
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Module 6, Lesson 1
Name_____________________________________
Directions: For each statement below
a) State the random trial
b) State the event, and give a letter to represent the event
c) Write the statement using probability notation (give the answer using all three forms: decimal,
percent, and fraction notation)
Example:
There is a 30% chance that the mayor will get re-elected.
a) The random trial is the election
b) The event is “the mayor gets re-elected”. Let’s call this event R (for re-elected)
c) P(R) = 0.3
Exercises
1. There is a 75% chance of rain tomorrow
2. The Seattle Seahawks have an 80% chance of getting to the playoffs
3. The chances of rolling a two is 1 out of 36 (hint: write the answer as a fraction)
4. If I flip a coin, there is a 50% chance of getting heads.
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Directions: Let the random trial be rolling 2 dice. Compute the following probabilities. Use the dice chart
from this lesson to count the number of ways the event can occur, then divide by 36. Write your answer
using probability notation (such as P(X=4)) and write your answer in decimal, fraction, and percent form.
5. The probability of rolling a 6
6. The probability of rolling a 12
7. P(rolling a 2)
8. P(rolling a 3)
9. P(X = 9)
10. P(X = 4)
11. P(rolling a number more than 10)
12. P(rolling a number less than 5)
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Module 6, Lesson 2
Name_____________________________________
1. A bag contains 5 purple marbles and 7 orange marbles. You pick one marble at random, note
the color, then put it back in the bag.
A) What is the probability of picking a purple marble?
B) If you repeated this trial 1,200 times, approximately how many purple marbles would you
pick?
2. A bag contains 9 purple marbles and 3 orange marbles. You pick one marble at random, note
the color, then put it back in the bag.
A) What is the probability of picking a purple marble?
B) If you repeated this trial 1,200 times, approximately how many purple marbles would
you pick?
3. A baseball player has been “at bat” (i.e. attempted to hit the ball) 369 times. He has hit the ball
165 times. What is this player’s probability of hitting the ball? Is this an empirical or theoretical
probability?
4. A football player has caught the ball 67 times out of 192 attempts. What is this player’s
probability of catching the ball? Is this an empirical or theoretical probability?
5. If you roll one die, the probability of rolling a five is 1/6. If you rolled the die 6000 times,
approximately how many times would you predict rolling a five?
6. If you roll one die, the probability of rolling a two is 1/6. If you rolled the die 3000 times,
approximately how many times would you predict rolling a two?
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7. A car insurance company knows the probability of a person getting in a car accident is 5%. If the
insurance company insures 4,000.000 customers, approximately how many of them will be
involved in a car accident?
8. A fire insurance company knows that there is a 0.2% chance of a fire. If the company insures
2,000,000 homes, approximately how many fires will there be?
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Module 6, Lesson 3
1.
Name_____________________________________
A coin is flipped three times. What is the probability that exactly two tails come up? Circle
the appropriate outcomes below, and calculate the answer:
HHH HHT HTH HTT THH THT TTH TTT
2. A coin is flipped three times. What is the probability that exactly one head comes up? Circle
the appropriate outcomes below, and calculate the answer:
HHH HHT HTH HTT THH THT TTH TTT
3. A coin is flipped 2 times. Write out the sample space, then calculate the probability of
getting 2 tails.
4. Suppose you are rolling two 7 sided dice, each with the numbers 1-7 for sides.
A) How many possible outcomes are there?
B) List all the possible outcomes: (Hint: It may help to think as Die #1 as red, Die #2 as blue)
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C) List the theoretical probability of rolling a…
2__________
8__________ 12__________ 14__________
number less than 5 __________
number greater than 5, but less than 10 __________
NOT rolling a 5 __________
5. The PIN (personal identification number) of a debit card has 4 digits. If a thief has one
chance to guess the correct PIN, what is the probability of a correct guess?
6. Some debit cards have a 6-digit PIN. If a thief has one chance to guess the correct PIN, what
is the probability of a correct guess?
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Module 6, Lesson 5
(note: no assignment from Lesson 4)
Name_____________________________________
1. A bowler has a 25% chance of getting a strike (knocking all the pins down in one roll of the ball), and a
35% chance of getting a spare (knocking all the pins down in two rolls).
a) What is the probability of not getting a spare?
b) What is the probability of getting a strike or a spare?
1. A baseball player has a 30% chance of hitting the ball, and a 10% chance of getting a strike-out.
a) What is the probability of getting a hit or a strike-out?
b) What is the probability of not striking out?
2. A special 4-sided die, labeled A, B, C, and D, has the following probabilities: P(A) = 0.3, P(B) = 0.4, P(C)
= 0.1, P(D) = 0.2. Is this a valid set of probabilities, based on the rules of probability? Why or why not?
3. A special 4-sided die, labeled A, B, C, and D, has the following probabilities: P(A) = 0.3, P(B) = 0.3, P(C)
= 0.3, P(D) = 0.3. Is this a valid set of probabilities, based on the rules of probability? Why or why not?
4. When playing Toss the Pigs, what is the probability that a pig lands on a side (either the left or right
side)?
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5. When playing Toss the Pigs, what is the probability that a pig does not land on a side (neither the left
nor right side)?
6. When rolling two dice, what is the probability of not getting a 12?
7. When rolling two dice, what is the probability of not getting a 7?
8. A bag contains 5 red marbles, 4 green marbles, 2 yellow marbles and 6 blue marbles. Use the rules of
probability to compute the following:
a) The probability of not getting a green marble
b) The probability of getting a green or red marble
c) Show that the sum of all the probabilities is 1. (in other words, show that P(red) + P(green) + P(yellow)
+ P(blue) = 1
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9. A bag contains 3 red marbles, 6 green marbles, 5 yellow marbles and 1 blue marble. Use the rules of
probability to compute the following:
a) The probability of not getting a green marble
b) The probability of getting a green or red marble
c) Show that the sum of all the probabilities is 1. (in other words, show that P(red) + P(green) +
P(yellow) + P(blue) = 1
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Module 6, Lesson 6
Name_____________________________________
1. A quiz has 3 true/false questions. If a student doesn’t know the answers and just randomly guesses,
what is the probability that all 3 questions are answered correctly?
2. A quick quiz consists of a multiple-choice question with 5 possible answers followed by a multiplechoice question with 6 possible answers. If both questions are answered with random guesses, find the
probability that both responses are correct.
3. Suppose that 13% of people own dogs. If you pick two people at random, what is the probability that
they both own a dog?
4. Suppose 25% of people prefer Pepsi over Coke. If two people are chosen at random, what is the
probability that both prefer Pepsi over Coke?
5. A bag contains 4 red tiles, 5 blue tiles, and 3 white tiles.
Compute the probability of the following events
a) Drawing a red tile
b) Drawing two red tiles in a row (without replacement)
c) Drawing two red tiles in a row (with replacement)
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d) Drawing two tiles and neither one being red (hint: not getting red twice in a row); with
replacement
e) Drawing two tiles and neither one being red (hint: not getting red twice in a row); without
replacement
6. A bag contains 7 red tiles, 6 blue tiles, and 2 white tiles. Compute the probability of the following
events:
a) Drawing a red tile
b) Drawing two red tiles in a row (without replacement)
c) Drawing two red tiles in a row (with replacement)
d) Drawing two tiles and neither one being red (hint: not getting red twice in a row); with
replacement
e) Drawing two tiles and neither one being red (hint: not getting red twice in a row); without
replacement
50
Module 6, Lesson 7
Name_____________________________________
1. Let the trial be flipping 3 coins. Below is the sample space:
HHH HHT HTH HTT THH THT TTH TTT
Let the random variable X = the number of tails (out of 3 coins). Complete the probability distribution
below:
X
Probability
(fraction form)
Probability
(decimal form)
0
1
2
3
2. Make a histogram of the probability distribution from the previous question.
3. Suppose there is a pair of special dice, each with 4 sides. Let X = the sum of the two dice. (the lowest is
double-ones, where X = 2, the highest is double-fours, where X = 8). Write the sample space, make a table
showing the probability distribution, then make a histogram.
51
52
Module 6, Lesson 8
Name_____________________________________
Suppose a person is selected at random and is asked how many movies he or she goes to per month. Let
the random variable X = the number of movies a person watches goes to in one month. Below is a
probability distribution.
Number of Movies
Probability
0
0.10
1
0.10
2
0.24
3
0.30
4
0.14
5
0.12
1. Explain what P(X=2) means, then give the probability
2. Explain what P(X < 3) means, then compute it
3. Make a histogram of this probability distribution, then describe the center, shape, and spread.
4. What is the area of the bar centered at 2? Explain why this is the same as the answer to question 1.
53
54
Module 6, Lesson 9
Name_____________________________________
1. A dart will hit somewhere on the grid below. Find the probability of hitting the stop-sign.
55
56
Module 6, Lesson 10
Name_____________________________________
Machine parts eventually wear out and need to be replaced. But the exact time until it needs to be
replaced is random. A few wear out immediately (perhaps because it was faulty), some will last 2 or 3
years, and still others may last 10 years or more. The figure below shows the probability distribution for
a particular machine part:
Here is the same graph, with the areas written in each one-year slice:
1. Add up the areas of each of the slices. What is the total?
2. What is the probability that the machine part will last between 2 and 4 years?
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3. What is the probability that the machine part will last between 1 and 3 years?
4. What is the probability that the machine part will last between 5 and 8 years?
5. What is the probability that the machine part will last between 1 and 4 years?
6. What is the probability that the machine part will last longer than 6 years?
7. What is the probability that the machine part will last less than 2 years?
8. Describe the center, shape and spread of the histogram. Explain what the center means, in terms of
probability.
58
Module 6, Lesson 12
Name_____________________________________
(Note: no assignment for Lesson 11)
Newborn babies (full-term, healthy, singleton) have an approximately normal distribution with a mean
of 3.6 kg and a standard deviation of 0.5 kg.
1. Make a sketch of the distribution below:
2. Fill in the blank: About 68% of the babies are between _____ and ______ kg.
Shade in the area on this normal curve that represents the answer:
3. What percentage of newborns weigh between 2.6 and 4.6 kg?
Shade in the area below that represents the answer:
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4. . What percentage of babies weigh more than 4.6 kg? Shade in the area below that represents
the answer:
5. What percentage of full-term, healthy, singleton babies weigh more than 4.1 kg?
6. What percentage of full-term, healthy, singleton babies weigh less than 2.6 kg?
60
Module 6, Lesson 13
1
Name_____________________________________
The Westwood Warrior basketball team wants to score more points. To get better at scoring points
the team is trying to improve its offensive strategies. Some opponents primarily use a zone defense,
while others primarily use a man-to-man defense. When the Warriors play against teams that use a
zone defense they score an average of 67 points per game. When they play against teams that use a
man-to-man defense they score an average of 62 points per game. The standard deviations are 8
and 5, respectively. Since the Warriors started using their improved offensive strategies they have
played two games with the following results.
Against the McNeil Mavericks
Maverick defense: zone
Warrior points: 77
Against the Round Rock Dragons
Dragon defense: man-to-man
Warrior points: 71
Which offensive strategy – learning to play against the zone defense or learning to play against the
man-to-man defense– appears to have improved the most? (Of course, there are many factors
involved in playing basketball. For your answer, assume the difference is due to the new offensive
strategies.)
2
The GPAs of students at Mt. San Antonio College are normally distributed with a mean equal to 3.0
and standard deviation 0.3.
A
The tick marks on the x-axis of the graph below are one standard deviation apart. Label the axis
with the appropriate values. Put the Z-score of each value below its x-value. Also label each
region of the graph with the area for that region. Use the Empirical Rule to help you with this
problem.
x
61
B
What is the probability that a random Mt. San Antonio College student has a GPA greater than
3.3?
C
What is the probability that a random Mt. San Antonio College student has a GPA between 2.1
and 2.7?
D
What is the probability that a random Mt. San Antonio College student has a GPA less than 3.6?
E
Would it be unusual to randomly encounter a student at this college with a GPA less than 2.52?
3
Suppose the mean of all adult males is 69 inches, and the standard deviation is 3 inches
A If a male is 55 inches tall, what is his z-score?
B If a male is 74 inches tall, what is his z-score?
C If a male is 71.7 inches tall, what is his z-score?
4. Suppose the mean height of all adult females is 64 inches, and the standard deviation is 3 inches.
A. If a female is 61 inches tall, what is her z-score?
B. If a female is 72 inches tall, what is her z-score?
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Module 6, Lesson 14
Name_____________________________________
Normal curve practice problems
For questions 1-5, use the following information: The mean weight of a newborn baby (healthy, fullterm, singleton) is 3.6 kg, with a standard deviation of 0.5 kg. The distribution is approximately normal.
1. Make a sketch of the distribution of newborns.
2. What percentage of newborns weigh more than 3.0 kg? Convert to z-scores, shade in the area
that represents these babies on the standard normal curve below, then use the table to answer
the question.
3. What percentage of babies weigh less than 3.0 kg?
4. What percentage of newborns weigh between 3.0 and 4.0 kg? Convert to z-scores, shade in the
area that represents these babies on the standard normal curve below, then use the table to
answer the question.
5. Suppose that any newborn that weighs less than 2.0 kg is considered high-risk and is given extra
medical attention. What percentage of newborns would this be?
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For problems 6 - 12, use the following information: the speed limit on a stretch of country road is
55 miles per hour (mph). A device used to measure the actual speed of cars traveling on the road finds
the distribution of speeds to be approximately normal with a mean of 55 and a standard deviation of 5.
6. Make a sketch of the distribution
7. What is the probability that a randomly selected car on this road is traveling between 45 and 65 mph?
Find the probabilities using the Empirical Rule. Then find the answer by converting to z-scores and
using the table. Do the answers agree?
8. What is the probability that a randomly selected car on this road is traveling between 55 and 60 mph?
Find the probabilities using the Empirical Rule. Then find the answer by converting to z-scores and
using the table. Do the answers agree?
9. What is the probability that a randomly selected car on this road is traveling above 50 mph? Find the
probabilities using the Empirical Rule. Then find the answer by converting to z-scores and using the
table. Do the answers agree?
10. What is the probability that a randomly selected car on this road is traveling faster than the speed
limit?
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11. What is the probability that a randomly selected car on this road is traveling faster than 71 mph?
12. What is the probability that a randomly selected car on this road is traveling slower than 62 mph?
13. A fish, commonly known as Red drum, (sciaenops ocellatus), is a popular coastal recreational fishing
catch. A reasonable estimate of the mean length of red drum caught, tagged, and released is 15.4
inches with a standard deviation of 4.5 inches. Current regulations by Texas Parks and Wildlife only
allow red drums between 20 and 28 inches to be kept. Fish outside this range must be thrown back.
Assuming the distribution of lengths is approximately normally distributed, what is the probability a
red fish caught on the Texas coast can be brought home for dinner?
For problems 14-15, use the following information: the time students took to complete a statistics test is
approximately normally distributed with a mean of 74 minutes and a standard deviation of 8 minutes.
14. What proportion of students took more than one hour to complete the test?
15. What is the probability a student needed between 70 and 80 minutes to complete the test?
65
For problems 16-17, use the following information: the distribution of heights of American women aged
18 to 24 is approximately normally distributed with mean 65.5 inches and standard deviation 2.5 inches.
16. What percentage of women are shorter than 5 feet (60 inches)?
17. The Tall Club International (www.tall.org) is a social organization for tall people. Any woman who is
at least 5’ 10 is eligible to join. What percentage of women aged 18-24 may join this club? (hint:
convert to inches first)
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Module 6, Lesson 15
Name_____________________________________
Directions: For questions 1-5, use the following information: The mean weight of a newborn baby
(healthy, full-term, singleton) is 3.6 kg, with a standard deviation of 0.5 kg. The distribution is
approximately normal.
1. If a newborn’s weight is in the 10th percentile (in other words, 10% of babies weigh less, 90% weigh
more), then how much does the baby weigh? Also, make a sketch of the normal curve and shade in
the region that would represent the lightest 10% of newborns.
2. What is the first quartile? (in other words, 25% of babies weigh less than what?) Also, make a sketch
of the normal curve and shade in the region that would represent the lightest 25% of newborns.
3. If a newborn is in the 80th percentile, how much does the baby weigh? Also, make a sketch of the
normal curve and shade in the region that would represent the lightest 25% of newborns.
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4. The heaviest 20% of newborns weigh more than what? (hint: look at the last question)
5. The heaviest 5% of newborns weigh more than what? Also, make a sketch of the normal curve and
shade in the region that would represent the heaviest 5% of newborns.
6
The time students took to complete a statistics test follows a distribution that is approximately
normal. The mean was 74 minutes. The standard deviation was 8 minutes.
A
What proportion of students took more than one hour to complete the test? (this is a review of
the last lesson)
B
What is the probability that a student needed between 70 and 80 minutes to complete the test?
(this is a review of the last lesson)
C
How long did it take the fastest 5% of the students to complete the test?
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7 Recreational fishers enjoy fishing for the Red Drum fish. In order to check on the population,
scientists often catch the fish, tag them, and then release them back into the water. The mean
length of the Red Drum fish that they measure is 15.4 inches with a standard deviation of 4.5 inches.
A
If you wanted to know the length, which separates the top 2% (longest Red Drum fish) from the lower
98%, (the rest of the Red Drum fish) what Z-score would you use?
B
How long would the top 2% of the Red Drum fish be?
69
70
More practice
using the Empirical (68-95-99.7) Rule
Name_______________________________
A biologist is doing research on squirrels. She finds that the mean weight of a squirrel is 550 grams, with
a standard deviation of 50 grams. Assume the population has a normal distribution. Answer the
following questions:
1. Sketch the distribution. Include the weights, and then the z-scores, underneath
2. What percentage of squirrels weigh between 500 and 600 grams?
3. What percentage of squirrels weigh between 450 and 650 grams?
4. 99.7% of squirrels weigh between ______ and ______
5. What percent of squirrels weigh more than 600 grams?
6. What percent of squirrels weigh less than 600 grams?
7. What percent of squirrels weigh more than 650 grams?
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8. What percent of squirrels weigh more than 700 grams?
9. What percent of squirrels weigh less than 550 grams?
10. What percent of squirrels weigh more than 550 grams?
11. What percent of squirrels weigh less than 650 grams?
12. What percent of squirrels weigh less than 700 grams?
13. What percent of squirrels weigh between 650 and 700 grams?
14. What percent of squirrels weigh between 550 and 600 grams?
15. What percent of squirrels weigh between 550 and 650 grams?
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More practice
Name___________________________________
using the Table of Standard Normal Curve Tail Probabilites
A biologist is doing research on squirrels. She finds that the mean weight of a squirrel is 550 grams, with
a standard deviation of 50 grams. Assume the population has a normal distribution. Answer the
following questions:
1. Sketch the distribution. Include the weights, and then the z-scores, underneath
1. What percentage of squirrels weigh more than 410 grams?
2. What percentage of squirrels weigh less than 410 grams?
3. What percentage of squirrels weigh more than 618 grams?
4. What percentage of squirrels weigh less than 593 grams?
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5. What percetage of squirrels weigh between 589 and 684 grams?
6. What percentage of squirrels weigh between 490 and 540 grams?
7. What percentage of squirrels weigh between 420 and 600 grams?
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Module 6 Review Questions (Write answers on your own paper)
1. If two dice are rolled, what is the probability that the sum of the two dice is 9?
2. Explain the difference between theoretical and empirical probability
3. Express the following sentence using probability notation: The gambler has a 5% chance of winning
the game. (Use W for “win”)
4. In the past year, 450 out of 12,000 drivers have been involved in a collision. Assuming that the driving
habits of the drivers are the same, what is the probability that a driver is involved in a collision this year?
5. Suppose there is a new game “Toss the Cow”, and the probability that a cow lands on its feet is 35%
and the probability that a cow lands on its side is 20%.
a) What is the probability of not landing on its side?
b) What is the probability of landing on its feet or side?
c) If a cow is tossed 5000 times, approximately how many times would the cow land on its feet?
d) If two cows are tossed, what is the probability that they both land on their feet? Is this an example of
independent or dependent events?
6. A bag contains 4 brown tiles, 3 green tiles, and 5 blue tiles.
a) What is the probability of randomly picking a brown tile?
b) What is the probability or randomly picking a brown or green tile?
c) If two tiles are picked (without replacement), what is the probability of getting 2 blue tiles? Is this an
example of independent or dependent events?
d) If two tiles are picked (with replacement), what is the probability of getting 2 blue tiles?
7. Many credit cards have a 3-digit security code on the back. What is the probability of randomly
guessing the code?
8. Suppose a game has the following probability distribution:
Points
Probability
0
0.40
1
0.30
2
0.2
3
0.1
a) Is this a legitimate probability distribution? Why or why not?
b) What is the probability that a player wins at least 2 points?
c) Let X = the number of points. Compute and explain P( 1< X < 4)
9. Suppose a student has a 70% chance of answering a question correctly on a test.
a) What is the probability that he or she will answer all 3 of the questions correctly? (out of 3
questions)
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10. Wildlife biologists believe the weights of adult trout can be described by a normal model. They
collect data from fishermen, and find that the mean weight is 2.8 kilograms, and the standard deviation
is 0.6 kilograms.
a) Sketch the graph of the normal curve. Include 3 standard deviations above and below the mean.
b) Use the 68-95-99.7 rule to estimate the percentage of trout that weigh less than 2.2 kg.
c) if a trout weighed 1.2 kilograms, what would be its z-score?
d) What percentage of trout weigh more than 4.0 kg?
e) What percentage of trout weigh between 2.0 and 3.0 kg?
11) In a large bag of candy, 30% of the pieces are green, 20% of the pieces are red, and the rest are
white.
a) What is the probability that a randomly chosen piece is white?
b) What is the probability that a randomly chosen piece is not red?
c) If you chose two pieces at random, what is the probability that both are red?
12. Make a probability distribution for flipping two coins. Let X = the number of heads
13. (multiple choice) Amanda’s little sister, Katie, is in high school. She recently had to take semester
exams. Her scores are in the table. Katie is upset because she thinks she did the worst in math but it is
usually her best subject! Which of the following statements is true about her scores?
Subject
English
History
Math
Science
Mean Score
70
83
60
85
Deviation
7
6
5
8
Katie’s Score
77
80
70
85
a. Katie did worse in English since that standard deviation is larger than the rest.
b. The score of 70 on math is a really good score since it’s 2 standard deviations above the mean
score.
c. The score of 85 in science is the “best” score since it is the highest score and not below the mean.
d. The score of 80 on History is the most impressive performance since it is close to the mean score.
14. (multiple choice) On a national standardized exam, the scores follow a normal distribution with a mean
of 60 and a standard deviation of 13. What is the probability that a student will receive a score between
73 and 86?
76
a.
Less than 3%
b. 13.5%
c. 47.5%
d. 68%
15. Professor Lopez has a newly collected data set. The data set is normally distributed. The mean of
the data is 102 and the standard deviation is 11. Within what interval will 68% of the data fall?
a. (91, 113)
b. (102, 113)
c. (102, 124)
Answers to Module 6 Review Questions
9. 0.343
10a.
10b. 16%
10c. -2.67
10c. 2.5% (2.2% is also acceptable)
10d. 53.9%
11a. 50%
11b. 80%
11c. 0.04
12
x
0
1
2
Probability
0.25
0.50
0.25
13. B (hint: compare the z-scores)
14. B
15. A
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d. (80, 124)
Practice problems for the Module 1-6 Assessment
1. Two researchers are studying fashion trends of college students at a particular college
campus. Researcher A decides to sit in a common area on campus and take notes on what she
sees students wearing. Researcher B decides to take a random sample of the students that
attend the college and survey them to determine trends. Which researcher’s method describes
an observational study?
a. Researcher A
b. Researcher B
c. Neither Researcher A nor Researcher B
d. Both Researcher A and Researcher B
2. Anti-smoking laws have changed the ways that people experience restaurants, bars, and
other public venues. Air quality studies have been conducted at several hotels, restaurants and
venues. These studies have shown that soon after these anti-smoking laws took effect, the level
of dangerous pollutants in the air of hotels, restaurants, and other public and entertainment
spaces were reduced by about 85%. One hospital conducted a study that examined the impacts
of dangerous pollutants in the air in the local community. The study found that heart attack
casualties dropped approximately 60% six months after the smoking ban was put into place.
(Statistics, 2009)Which of the following best describes this study?
a. This was an observational study; therefore we can conclude that Anti‐smoking laws reduced
the percentage of heart attack casualties.
b. This was an observational study; therefore we cannot conclude that Anti‐smoking laws
reduced the percentage of heart attack casualties.
c. This was an experiment; therefore we can conclude that anti‐smoking laws reduced the
percentage of heart attack casualties.
d. This was an experiment; therefore we cannot conclude that Anti-‐‐smoking laws reduced the
percentage of heart attack casualties.
3. In City A, housing prices ranged from $120,000 to $600,000. In City B, housing prices ranged
from $150,000 to $$950,000. Which city MOST LIKELY has the higher standard deviation?
a. City A
b. City B
c. Impossible to tell
d. Both would have the same standard deviation
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4. “One hospital in California conducted a study and found that heart attack casualties dropped
after a smoking ban was put into place.” (Statistics, 2009) Identify the DATA collected, and
CLASSIFY it as categorical or quantitative:
a. DATA: smoking ban; CLASSIFICATION: quantitative
b. DATA: smoking ban; CLASSIFICATION: categorical
c. DATA: heart attack casualties; CLASSIFICATION: categorical
d. DATA: heart attack casualties; CLASSIFICATION: quantitative
5. A study of the effects of the acai berry was done to determine if the berry has any effect on
promoting weight loss. The researchers surveyed people who were participating in a weight
loss program. The survey asked whether the people had consumed, that is eaten or drunk, any
acai berry products and, if so, how often they consumed acai berry products. The researchers
concluded that the acai berry had no effect on weight loss because there was no significant
difference in weight loss between those who consumed the acai berry and those who did not. Is
the researchers’ conclusion valid?
a. Yes. This study was based on an experiment.
b. No. The subjects volunteered to be studied.
c. Yes. There was no significant difference in weight loss found between those that consumed
products containing the acai berry and those who did not.
d. No. This was an observational study; therefore we cannot draw cause‐effect conclusions.
6. In an experimental study to investigate the effects of particular antiviral medication, 30
people were randomly assigned to the treatment group and another 30 people were randomly
assigned to the control group. In this study, what is the purpose of random assignment?
a. To ensure only one group is a control group.
b. To ensure results will apply to the larger population.
c. To ensure an equal number of people in the treatment and control group.
d. To ensure no real difference between the two groups prior to the application of the
treatment.
Questions 7 and 8 are based on the following situation:
Students in an introductory statistics course took their first exam. Before the instructor
returned their exams, students were asked to complete a survey. In this survey, students were
asked "Rate how well you think you did on your first exam" where 1 = “Very Poorly” and 10 =
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“Very Well”. The instructor examined the survey data and needs to interpret the results. Below
is a histogram of the students’ responses:
7. What do students’ survey responses tell the instructor about how successful they think they
were on the exam?
a. All of the students thought that they did either poorly or well on the exam.
b. A majority of students in the class feel that they did well on the exam although a few feel
they did not do very well.
c. The instructor should remove the five students with the lowest ratings to have an
approximately normal distribution.
d. Most of the students feel that they didn’t do too well on the exam.
8. What is the relationship between the mean and median?
a. the mean is greater than the median
b. the mean is less than the median
c. the mean is approximately equal to the median
d. there is no way to estimate the mean and median
Questions 9-11 are based on the following situation:
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A study has been done to determine if there is a link between the number of colas that
American women consumed each week and their bone mineral density (in g/cm²). The
researcher asked women how many colas they consume each week. The researcher also
measured the women’s bone mineral density. The researcher recorded her data in a
scatterplot. The following scatterplot shows the relationship between the number of colas
consumed per week and the bone mineral density.
9. Using the data in the scatterplot, choose the BEST interpretation of the relationship between
the two variables.
a. The scatterplot shows very little, if any relationship between number of colas consumed per
week and the bone mineral density of women.
b. The scatterplot shows a moderate linear relationship between number of colas consumed
per week and the bone mineral density of women.
c. The scatterplot shows a strong linear relationship between number of colas consumed per
week and the bone mineral density of women.
d. It is impossible to say without more information.
10. Which is the most likely equation for the least-squares regression line?
a. predicted bone mineral density = 0.89 – 0.005(number of colas consumed)
b. predicted bone mineral density = 0.89 + 0.005(number of colas consumed)
c. predicted bone mineral density = - 0.89 – 0.005(number of colas consumed)
d. predicted bone mineral density = -0.89 + 0.005(number of colas consumed)
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11. The correlation is…
a. Close to 1
b. Close to 0
c. Close to -1
d. Impossible to tell
12. This graph shows how many students are enrolled in each class at a local university.
Which of the following conclusions is valid?
a.
b.
c.
d.
There are more students taking Physics than Economics
There are more than twice as many students taking Economics than Physics
There are more than twice as many students taking Political Science than Chemistry
There are more Psychology students than Political Science students
Questions 13-15 are based on the following situation:
Wildlife conservationists are often interested in understanding patterns, or trends, for
different wildlife. Recently, they have been monitoring the growth patterns of the female
Appalachian Black Bear. Bears are large so gathering data about bears can be difficult. The
researchers wanted to determine if they could figure out the weight of a bear if they already
knew the bear’s length. They randomly selected 26 female black bears out in the wild and
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found their lengths (in cm) and their weights (in kg). The following scatterplot shows the
relationship between the length of the female black bear and the weight along with the least
squares regression line. Which of the following statements provides the best interpretation of
the slope and the regression line?
13. The slope of the regression line indicates:
a. For every 10 cm increase in the black bear’s length, the bear’s predicted weight
increases by 1.765 kg.
b. For every 1 cm increase in the black bear’s length, the bear’s predicted weight
increases by 1.765 kg.
c.For every 10 cm increase in the black bear’s length, the bear’s predicted weight decreases by
156 kg.
d.For every 1 kg increase in the black bear’s predicted weight, the bear’s length increases by 1.7
65 cm.
14. What is the most accurate prediction for a bear whose length is 135 cm?
a. 82.3 kg
b. 104.1 kg
c. 394.3 kg
d. 80.0 kg
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15. Using the regression line, it was predicted that a bear would weigh 95.4 kg. The residual was
-4.9 kg. What was the bear’s actual weight?
a. 100.3 kg
b. 90.5 kg
c. Impossible to tell
Questions 16-17 refer to the following situation:
A population of wild dogs have grown according the formula
yˆ  45.9(1.34) x
Where x is the years since 1990.
16. What does the number 1.34 indicate?
a. the population of dogs has been increasing by 1.34% per year
b. the population of dogs has been increasing by 134% per year
c. the population of dogs has been increasing by 34% per year
d. the population of dogs has been decreasing by 66% per year
17. What is the population of dogs in 2010?
a. 1,230
b. 15,992
c. 73
d. 348
18. If a coin is tossed 100 times, it will land on heads:
a. exactly 50 times.
b. at least 50 times.
c. at most 50 times.
d. approximately 50 times.
19.On a national standardized exam, the scores follow a normal distribution with a mean of 60
and a standard deviation of 13. What is the probability that a student will receive a score
between 73 and 86?
a. Less than 3%
b. 13.5%
c. 47.5%
d. 68%
84
20.Professor Lopez has a newly collected data set. The data set is normally distributed. The
mean of the data is 102 and the standard deviation is 11. Within what interval will 68% of the
data fall?
a. (91, 113)
b. (102, 113)
c. (102, 124)
d. (80, 124)
21. The amount of a radioactive substance is currently 900 grams. It will decrease by a certain
percentage each year. Let x = the number of years since 2012.
800
600
400
200
x
5
10
15
20
25
30
35
40
45
Use the graph to estimate the amount of the substance in the year 2020.
a. 250 grams
b. 50 grams
c. 200 grams
d. 900 grams
22. John scored 56 points on a test. In his class, the mean score was 40, and the standard
deviation was 10. In another class, Bob scored 87 on his test, and the mean in his class was 70
and the standard deviation was 20. Who did better, and why?
a.
b.
c.
d.
Bob, because 87 is higher than 56
John, because his score was 16 points higher than the class mean
Bob, because his score is 17 points higher than the class mean
John, because is z-score is 1.6, while Bob’s z-score is 0.85
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Answers to Practice Questions
Question
Correct
response
brief explanation
1
D
neither researcher used any treatments
2
B
no treatment and no random assignment
3
B
the housing prices in city B have more spread
4
C
heart attack casualties are categorical: each individual can be put into a "yes" or
"no" category (either he/she gets a heart attack or he/she doesn't)
5
D
There are confounding variables, so since there is not random assignment, no
cause-effect conclusions can be made
6
D
Groups must be randomly assigned to so they are similar (so confounding variables
are controlled)
7
B
most rated themselves 6 through 10
8
B
the histogram is left-skewed. The few low scores bring down the mean
9
C
the dots form a near-perfect line
10
A
the y-intercept is 0.89 (positive) and the slope is -0.005 (negative)
11
C
because the direction is negative, and the points form a nearly perfect line
12
B
There are more than 300 students taking economics, and less than 150 taking
physics
13
B
The slope is 1.765 kg per cm (slope is "y per x")
14
A
1.765*135-156 = 82.3
86
15
B
Since the residual is negative, the actual point is below the line
16
C
1.34, take away the 1, and you have 0.34, which is 34%
17
B
in 2010, x=20 (20 years since 1990). 45.9(1.34)^20=15,992
18
D
with any random trial, nothing is ever exact
19
B
95% - 68%=27%, then divide by 2 to get 13.5%
20
A
91 is one standard deviation above the mean, 113 is one standard deviation below
the mean
21
A
x=8, then find the location of the curve when x=8
22
D
use z-scores to compare how each student did *in relation to his peers*
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Module 7, Lesson 3
Name_____________________________________
(note: no assignment for Lessons 1, 2 and 4)
1. Suppose, in an election for mayor, that Alicia Harper will get 48% of the vote, and her opponent will
get 52% of the vote.
a) If the sample size is 400, calculate the standard deviation of the sampling distribution, and make a
sketch of the sampling distribution.
b) Is it possible that a poll, taken on the day before the election, could indicate that Ms. Harper will win
the election?
c) If the sample size is 800, re-calculate the standard deviation of the sampling distribution and sketch
the sampling distribution. Would it be likely or unlikely that a poll would indicate that Ms. Harper will
win the election?
2. If you play "Pass the Pigs", suppose the probability that a pig lands on its feet is 20%.
a) If you toss a pig 200 times, about how many times would you expect the pig to land on its feet?
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b) Tossing a pig 200 times is equivalent to taking a sample of 200 pigs. Calculate the standard deviation
of the sampling distribution, then sketch the sampling distribution. Explain what this means.
c) Would it be surprising if the pig landed on its feet 35 out of 200 times? Why or why not?
d) Would it be surprising if the pig landed on its feet 20 out of 200 times? Why or why not?
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