Download Name: Math 9C - Greg`s PCC Math Page

Name:___________________
Date: 3/10/2011
STAT 50
Quiz 3
A formula you may need: P( A )  1  P( A)
1. (8 points) A bag contains 8 scrabble letters. The letters in the bag are:
E1 K5 J8 Q10 P3 C3 G2 I1
The procedure is to draw a single letter from the bag without looking in the bag. The
number next to each letter tells you how many points each letter is worth. Let A be the
event that a vowel is drawn and let B be the event that a letter worth 5 or more points is
drawn. Find
a) A
b) B
c) A
d) B
e) P( A)
f) P(B)
c) P ( A )
d) P (B )
2. (1 point) In order for the weatherman to determine if it is going to rain today, he
looked at past records and noticed that out of 1287 days in the past that had all the same
conditions as today has, it has rained on 821 of those days. What is the probability that it
rains today?
3. (1 point) If S denotes the sample space of a procedure, what is P(S ) ? Why?
Name:___________________
Date: 3/15/2011
STAT 50
Quiz 4
Some formulas you may need:
P( A )  1  P( A)
P( A  B)  P( A)  P( B)  P( A  B)
P( A  B)  P( A)  P( B | A)
P(at least one)  1  P(none)
1. (2 points) Consider the procedure where you draw a single card from a standard poker
deck. Let A be the event that you draw a diamond and let B be the event that you draw a
7. Find the probability that you draw a diamond or a 7.
2. (4 points) Suppose a bag contains 5 red balls, 3 green balls and 2 yellow balls.
Consider the procedure that you draw 2 balls from this bag one at a time without
replacement. Find
a) The probability that you draw a green ball first and then a yellow ball
b) The probability that you draw a red ball both times
3. (2 points) Consider the procedure where you draw 2 cards from a standard poker deck
without replacement. Find the probability that you get at least one ace.
4. (2 points) Consider the procedure where you spin the spinner below once. Let A be
the even that the spinner lands on a red number and let B be the event that the spinner
lands on an even number.
a) Are the events A and B disjoint? Why or why not?
b) Are the events A and B independent? Why or why not?
Name:___________________
Date: 3/17/2011
STAT 50
Quiz 5
1. (2 points) How many 7 character license plates are there where the 2nd, 3rd and 4th
characters are letters (A-Z), the rest of the characters are numbers (0-9), and no letter can
be used more than once (but the numbers can repeat).
2. (2 points) How many (distinguishable) permutations are there of the word BANANA?
3, (2 points) Out of a senior class of 20 students, 4 people are going to be picked to be on
the yearbook committee. How many different committee choices are possible?
4. (2 points) In horse racing, betting an exacta means picking which horse will come in
first and which will come in second in the correct order. How many different exacta bets
are possible in a 12 horse race?
5. (2 points) You have 5 books that you are going to arrange on a shelf. How many
different arrangements are possible?
Name:___________________
Date: 3/22/2011
Formulas you may need:
   xp(x)
STAT 50
Quiz 6
P( X  x)  n C x p x q n  x
 2   x 2 p( x)   2

 x
2

p ( x)   2
1. (2, 2, 2, 1 points) Suppose you are betting on the draw of a single card from a standard
poker deck. You will win $5 if you draw a heart, win $2 is you draw a spade, and lose $4
if you draw anything else. Let X stand for the amount of money you will win when
making this bet once.
a) Find the probability distribution of X
b) Find the mean of X
c) Find the standard deviation of X
d) What is the meaning of the mean of X?
2. (3 points) You have a bag with 4 green balls, 2 red balls and 1 yellow ball in it. You
draw 15 balls from this bag one at a time with replacement. What is the probability that
you draw a yellow ball exactly 3 times?
Name:___________________
Date: 4/05/2011
STAT 50
Quiz 7A,B
1. (1, 1, 1, 2, 2, 2, 1 points) Suppose Z has a standard normal distribution.
a) What are the possible values for Z?
b) What is the mean  of Z?
c) What is the standard deviation  of Z?
d) What is P( Z  2.37) ?
e) What is P( Z  0.49) ?
f) What is P(1.55  Z  0.36) ?
g) What is P( Z  1.83) ?
2. (2 points) State the requirements for a density curve.
3. (2 points) Suppose X is a random variable with the density curve drawn below.
a) What are the possible values of X?
b) What is P(1  X  7) ?
4. (2 points) Suppose X is uniformly distributed over the interval [3,13].
a) Find c that makes this a probability density.
b) Find P(0  X  7)
5. (4 points) Suppose the heights of 40 year old males is normally distributed with a mean
of 70 inches and a standard deviation of 6 inches. What is the probability that a randomly
selected 40 year old man’s height is between 64 inches and 76 inches? (Hint: Let X
denote the height of a 40 year old male)
Name:___________________
Date: 4/07/2011
Some formulas you may need:
STAT 50
Quiz 8
X  X
X 
X
n
1. (1, 2 points) Let X be the number face up on a die if a die is rolled once. Let X be the
average of the face up numbers on the die if the die is rolled twice. Find
a) P X  3
b) PX  3
2. (3 points) The Doritos chip company claims that the number of chips in their small
bags of Doritos has a mean of 20 chips and a standard deviation of 2 chips. What is the
probability that the average number of chips in a sample of 64 bags of chips is less than
19.5 chips.
3. (4 points) IQ scores of 18 year olds are normally distributed with a mean of 130 points
with a standard deviation of 5 points. Find
a) the probability that if one 18 year old is randomly selected, his or her IQ score will be
more than 132 points.
b) the probability that if nine 18 year olds are randomly selected, their average IQ score
will be more than 132 points.
Name:___________________
Date: 4/12/2011
STAT 50
Quiz 9
Some formulas you may need:
P X  x   n C x p x q n  x
  np
  npq
Make sure to answer the question below showing all work I have asked you to show for
such problems in class.
1. (10 points) A Boeing 767-300 aircraft has 213 seats. When someone buys a ticket for a
flight, there is a 0.0995 probability that the person will not show up for the flight (based
on data from an IBM research paper by Lawrence, Hong, and Cherrier). A ticket agent
accepts 236 reservations for a flight that uses a Boeing 767-300. Find the probability that
not enough seats will be available. Is this probability low enough so that overbooking is
not a real concern?
Name:___________________
Date: 4/14/2011
Some formulas you may need:
STAT 50
Quiz 10
E  z / 2
pˆ qˆ
n
E
z  / 2
n
1. (1, 3, 2 points) PCC is considering putting energy drink vending machines on campus.
Before they decide, the president of PCC wants to know what percentage of PCC
students drink energy drinks on a regular basis. To figure this out, the president asks his
favorite statistics professor Greg Miller to poll his stats class and get an estimate. Of the
35 students in Greg’s stats class, 7 say that they drink energy drinks on a regular basis.
a) What is the best point estimate for the percentage of all PCC students who drink
energy drinks on a regular basis?
b) Find a 95% confidence interval for the percentage of all PCC students who drink
energy drinks on a regular basis.
c) What does the 95% in a 95% confidence interval mean?
2. (1, 3 points) To estimate the average amount of money that people take when they go
to a casino, Morongo asked 100 of its visitors how much money they brought with them
to the casino. The average amount of money that these 100 people brought with them was
$130. Assume that the standard deviation of the amount of money that all casino visitors
bring with them to the casino is $22 and assume that those who were polled told the truth.
a) What is the best point estimate for the average amount of money that casino goers
bring with them to the casino?
b) Find an 88% confidence interval for the average amount of money casino goers bring
with them to the casino
Name:___________________
Date: 5/02/2011
A formula you may need:
STAT 50
Quiz 11
z
pˆ  p
pq
n
1. (5 points) Cheating Gas Pumps When testing gas pumps in Michigan for accuracy,
fuel-quality enforcement specialists tested pumps and found that 1299 of them were not
pumping accurately (accurately means within 3.3 oz when 5 gallons are pumped), and
5686 pumps were accurate. Use a 0.01 significance level to test the claim of an industry
representative that less than 20% of Michigan gas pumps are inaccurate.
2. (5 points) Driving and Cell Phones In a survey, 1640 out of 2246 randomly selected
adults in the United States said that they use cell phones while driving. Use a 0.05
significance level to test the claim that the proportion of adults who use cell phones while
driving is equal to 75%.
Name:___________________
Date: 5/05/2011
Some formulas you may need:
STAT 50
Quiz 12
z
x

n
t
x
s
n
1. (5 points) Weights of Pennies The U.S. mint has a specification that pennies have a
mean weight of 2.5 g. A simple random sample of 37 pennies manufactured after 1983
was taken and those pennies have a mean weight of 2.49910 g and a standard deviation of
0.01648 g. Use a 0.05 significance level to test the claim that this sample is from a
population with a mean weight equal to 2.5 g.
2. (5 points) The Doritos company claims that the average number of chips in their small
bags of chips is 20 chips. A disgruntled consumer claims that Doritos is cheating their
customers and are putting less chips in their bags than they should. To this end, a sample
of 49 bags of chips is obtained and the average number of chips in this sample is 18.3
chips. Suppose that the standard deviation of the number of chips in all Doritos bags is
3.5 chips. Use a 0.01 significance level to test the claim that the mean number of chips in
small Doritos bags is less than 20 chips.
Extra Credit (5 points): Suppose you have data that is normally distributed with   32
and   7 .
a) 68% of the data will be between what two numbers?
b) What percent of the data will be between the numbers 18 and 46?
c) 99.7% of the data will be between what two numbers?
Name:___________________
Date: 5/10/2011
Some formulas you may need:
STAT 50
Quiz 13
2 
(n  1) s 2
2
1. (10 points) A can of Coke is supposed to contain 12 oz’s of soda. However, the amount
of soda in each can will vary somewhat. The Coca-Cola company claims that the
standard deviation of the amount of soda in their cans is 0.15 oz’s. To make sure that the
amount of soda in each can is consistent and that their machines used to fill the cans are
working properly, an inspector measures the amount of soda in 49 cans and finds that the
standard deviation of the sample is 0.21 ounces. Test the claim that the standard deviation
of the amount of soda in a can of Coke is larger than 0.15 oz’s at the 0.05 significance
level. Is the Coca-Cola company lying? Do their filling machines need upgrading?
Name:___________________
Date: 5/12/2011
Some formulas you may need: z 
STAT 50
Quiz 14
 pˆ 1  pˆ 2    p1  p 2 
pq pq

n1
n2
E  z / 2
pˆ 1qˆ1 pˆ 2 qˆ 2

n1
n2
1. (5 points) Adverse Effects of Viagra In an experiment, 16% of 734 subjects treated
with Viagra experienced headaches. In the same experiment, 4% of 725 subjects given a
placebo experienced headaches. Use a 0.01 significance level to test the claim that the
proportion of headaches is greater for those treated with Viagra. Do headaches appear to
be a concern for those who take Viagra?
2. (5 points) Adverse Effects of Viagra Using the sample data from problem 1, construct
the confidence interval corresponding to the hypothesis test conducted with a 0.01
significance level. What conclusion does the confidence interval suggest?
Name:___________________
Date: 5/24/2011
STAT 50
Quiz 15
Some formulas you may need:
r
b1 

n xy   x  y 


n  x   x 
2
n xy   x  y 



yˆ  b1 x  b0
n  y   y 
2
n  x 2   x 
2
2
2
 y  x    x  xy

n x    x 
2
b0
2
2
1. (5, 5) The data below are blood pressure measurements of 5 patients taken once from
their left arms and once from their right arms. Use x to denote a patient’s right arm blood
pressure and let y denote a patient’s left arm blood pressure.
Right Arm x
Left Arm y
a) Find r
102
175
101
169
94
182
79
146
79
144
b) Find the least squares regression line for the data
Extra Credit (5, 5 points)
a) Use the least squares regression line to predict a patient’s blood pressure in their left
arm if the blood pressure in their right arm is 100 mm Hg.
b) Use the least squares regression line to predict a patient’s blood pressure in their right
arm if the blood pressure in their left arm is 200 mm Hg.
Name:___________________
Date: 5/26/2011
STAT 50
Quiz 16
1. (5 points) In order to study global warming, the data below was taken over different
years (CO2 levels in parts per million and temperature in  C ).
CO2 x
Temperature y
314
13.9
317
14
320
13.9
326
14.1
331
14
339
14.3
346
14.1
354
14.5
361
14.5
369
14.4
After doing all the regression calculations, the equation of the least squares regression
line for this data is yˆ  10.483  0.0109 x . Construct a 95% prediction interval that
predicts what the temperature of the Earth will be if the CO2 level reaches 400 parts per
million.
2. (5 points) The table below lists the frequency of wins for different post positions in the
Kentucky Derby horse race. A post position of 1 is closest to the inside rail, so that horse
has the shortest distance to run. Use a 0.05 significance level to test the claim that the
likelihood of winning is the same for the different post positions. Based on the result,
should bettors consider the post position of a horse racing in the Kentucky Derby?
Post Position
Wins
1
19
2
14
3
11
4
14
5
14
6
7
7
8
8
11
9
5
10
11
Some formulas you may need:
se 
y
2
 b0  y  b1  xy
2
E  t / 2 s e
n2
E
n
k
n x 0  x 
1
1 
n n  x 2   x 2
E  pn

2  

O  E 2
E
Name:___________________
Date: 5/31/2011
STAT 50
Quiz 17
Some formulas you may need:
2  
O  E 
2
E



 row total  column total 


E
grand total
df  r  1c  1
1. (10 points) Which Treatment Is Better? A randomized controlled trial was designed
to compare the effectiveness of splinting versus surgery in the treatment of carpal tunnel
syndrome. Results are given in the table below. The results are based on evaluations
made one year after the treatment. Using a 0.01 significance level, test the claim that
success is independent of the type of treatment. What do the results suggest about treating
carpal tunnel syndrome?
Splint Treatment
Surgery Treatment
Successful Treatment
60
67
Unsuccessful Treatment
23
6
Name:_____________________
Date: 3/03/2011
STAT 50
Exam 1
Please show ALL your work on the problems below. No more than 1 point will be
given to problems if you only provide the correct answer and insufficient work.
Some formulas you may need:
x
x
n
 x  x 
s
n 1
n x 2   x 
2
2

n(n  1)
1. (7, 7, 7, 7, 7, 13, 7 points) Consider the data below:
Data = 5, 8, 9, 9, 12, 14, 22, 12, 8, 8
a) Find the mean of the data
b) Find the median of the data
c) Find the mode(s) of the data
d) Find the midrange of the data
L
r
n
100
(this is a continuation of question 1)
e) Find the range of the data
f) Find the standard deviation of the data
g) Find the variance of the data
2. (20, 7, 10 points) Consider the data below:
Data = 10
60
13
89
14
101
18
121
19
122
21
184
27
211
28
289
30
327
44
505
a) Find the 5-number summary for this data
b) Draw a box plot for this data
c) Let s1 denote the standard deviation of the first 10 numbers of the data and let s2
denote the standard deviation of the last 10 numbers of the data. Without calculating s1
or s2 , which one do you think will be bigger? Explain as clearly as possible. (Hint: Look
at your box plot in part (b))
3. (24 points) Define and explain the difference between
a) a Population and a Sample
b) a Single Blind and a Double Blind Experiment
c) a Random Sample and a Simple Random Sample
d) Stratified Sampling and Cluster Sampling
4. (24 points) The data below are the ages of the students in my Pre-Algebra class at
Valley College:
Data: 30 31 18 36 28 33 32 41 26 34
42 38 21 32 34 31 31 19 25 22
47 25 34 35 37
Use classes of width 5 and start your first class at 15 to
a) Make a frequency table
b) Make a relative frequency table
c) Make a relative frequency histogram
d) Is the distribution of this data a Normal Distribution? Explain clearly why or why not.
5. (5 points) What is the main idea of statistics?
6. (5 points) Give an example of a voluntary response sample.
Name:_____________________
Date: 3/24/2011
STAT 50
Exam 2
Please show ALL your work on the problems below. No more than 1 point will be
given to problems if you only provide the correct answer and insufficient work.
Some formulas you may need:
P( A )  1  P( A)
P( A  B)  P( A)  P( B)  P( A  B)
P( A  B)  P( A)  P( B | A)
E     xp(x)
P X  x   n C x p x q n  x
P X  x  

e 
x!
x
P(at least one)  1  P(none)
 2   x 2 p( x)   2
  np
 2  npq
2 
 

 x
2

p ( x)   2
  npq
1. (51 points) A box contains 8 colored balls with numbers on them as shown below.
Consider the procedure where you draw one ball out of the box.
a) What is the sample space? (Hint: To denote an outcome, it is ok to just use numbers)
b) Let B be the event that you draw a blue ball and let E be the event that you draw an
even number. Find the following:
B =
E =
B =
E =
BE =
(this is a continuation of problem 1)
BE =
c) Find the following probabilities
P (B ) 
P (E ) 
P(B ) 
P(E ) 
P( B  E ) 
P( B  E ) 
P( B | E ) 
P( E | B) 
d) Are the events B and E disjoint? Why or why not?
e) Are the events B and E independent? Why or why not?
2. (8, 8, 8 points)
a) How many 7 character license plates are there where the 2nd, 3rd, and 4th characters are
letters (A-Z), the other characters are numbers (0-9) and repetition is allowed?
b) How many 7 character license plates are there where the 2nd, 3rd, and 4th characters are
letters (A-Z), the other characters are numbers (0-9) where no number or letter can be
repeated?
c) If a 7 character license plate like the ones described in part (a) is chosen at random,
what is the probability that no letter or number is repeated?
3. (15 points) At the horse races, betting on an trifecta means that you bet on the which
horse comes in 1st, 2nd and 3rd in the correct order. Suppose the race you are betting on
has 8 horses and you bet on the 7-2-5 exacta (meaning you are betting that the number 7
horse will come in 1st , the number 2 horse will come in 2nd and the number 5 horse will
come in 3rd. Assuming all horses have the same chance of winning, what is the
probability that you win your trifecta bet?
4. (5, 15, 5 points) Suppose a gambler is making a bet on the outcome of drawing a single
card from a standard poker deck. Specifically, he will win $10 if he draws the Ace of
spades, he will win $5 if he draws any other Ace, he will win $3 if he draws any other
spade, and will lose $1 if anything else is draws.
a) Find the probability distribution for X.
b) Find the mean, variance and standard deviation of X.
c) Is it in the gambler’s best interest to play this game? Why or why not?
5. (15, 5 points) Suppose a scientist comes up with a drug that he feels cures the common
cold. He claims that the probability that his drug will cure a cold is 85%. The scientist
administers this drug to 8 people who currently have a cold.
a) Find the probability that exactly 5 of these people will be cured of their colds.
b) How many people can be expected to be cured out of the 8 people receiving the drug?
6. (15 points) For the last few years, Lucy has monitored how many calls she received
from 1-2pm on Saturday afternoons and concluded that she averages 3 calls during that
time. That is the probability that she will receive 5 calls from 1-2pm this coming
Saturday?
Name:_____________________
Date: 4/26/2011
STAT 50
Exam 3
Please show ALL your work on the problems below. No more than 1 point will be
given to problems if you only provide the correct answer and insufficient work.
Some formulas you may need:
x
x
n x 2   x 
s 
n
  npq
X  X
E

pq
z / 2
n
n  1s 2
 R2
2 
X 
E
n  1s 2
 L2
s
n(n  1)
 2  npq
  np

n
n x 2   x 
2
2
2
n(n  1)
Z
X 

X
n
E
z / 2
s
n
n  1s 2    n  1s 2
2
2
R
1. (6 points) List the requirements for a probability distribution.
L
t / 2
2. (8, 8 points)
a) Find the value of c that makes the graph below a probability distribution
b) Find P(3  X  9)
3. (7, 7 points) Consider the following probability distribution
a) What are the possible values of X?
b) Find P( X  12)
4. (10, 10, 10, 10 points) The heights of 40 year old males in Southern California are
normally distributed with a mean of 70 inches and a standard deviation of 5 inches.
a) Find the probability that a randomly selected 40 year old male from Southern
California has a height less than 63 inches.
b) Find the probability that a randomly selected 40 year old male from Southern
California has a height more than 80 inches.
c) Find the probability that a randomly selected 40 year old male from Southern
California has a height between 65 inches and 75 inches.
d) If 25 40-year old male from Southern California are randomly selected, what is the
probability that their mean weight is less than 68 inches?
5. (7, 13 points) The probability that a randomly selected person has red hair is 15%.
Suppose we randomly select 100 people.
a) Check to see if the conditions for approximating a binomial distribution using a normal
distribution are satisfied.
b) Find the probability that at least 20 of the 100 randomly selected people have red hair.
6. (7, 13 points) In order to find the percentage of people who have green eyes, you look
at a simple random sample of 200 people and find that 37 of them have green eyes.
a) What is the best point estimate of the proportion of people who have green eyes?
b) Find a 90% confidence interval for the proportion of people who have green eyes.
7. (6 points) Explain as clearly as possible what the 95% means in a 95% confidence
interval.
8. (10, 10, 10 points) In order to estimate the average SAT score of people at PCC, a
simple random sample of 51 PCC students was selected. The average SAT score in the
sample is 1009 points with a sample standard deviation of 85 point.
a) Assuming it is known that the standard deviation of the SAT scores of ALL PCC
students is 90 points, construct a 95% confidence interval estimate for the average SAT
score of all students at PCC.
b) Assuming that the standard deviation of the SAT scores of ALL PCC students is
unknown, construct a 95% confidence interval estimate for the average SAT score of all
students at PCC.
c) Assuming that the standard deviation of the SAT scores of ALL PCC students is
unknown, construct a 95% confidence interval estimate for the variance the SAT score of
all students at PCC.
Name:_____________________
Date: 5/17/2011
STAT 50
Exam 4
Please show ALL your work on the problems below. No more than 1 point will be
given to problems if you only provide the correct answer and insufficient work.
Some formulas you may need:
Z
Z
pˆ  p
pq
n
X 
t

n
2 
(n  1) s 2

E  z / 2
d  d
t
sd
n
F
n
z
2
s1
2
s2
2
X 
s
 pˆ 1  pˆ 2    p1  p 2 
pq pq

n1
n2
pˆ 1qˆ1 pˆ 2 qˆ 2

n1
n2
x
x
n
s
 
n x 2   x 
n(n  1)
2
1. (30 points) The U.S. mint has a specification that pennies have a mean weight of 2.5g.
A sample of 37 pennies all of whose dates are after 1983 was obtained and the mean
weight was 2.49910g with a standard deviation of 0.01648g. Use a 0.05 significance level
to test the claim that this sample is from a population with a mean weight equal to 2.5g.
2. (30 points) In order for the Sunchips company to determine that the number of chips in
their small bags is consistent, a quality control expert took a sample of 100 bags of chips
and counted the number of chips in each bad. The average number of chips in these 100
bags turned out to be 34.6 chips with a standard deviation of 2.4 chips. If the chip
industry, having a chip count standard deviation of 2 chips is desirable. Use a 0.05
significance level to test the claim that the standard deviation of the chip count is larger
than 2 chips.
3. (30 points) A scientist developed a pill that is supposed to help students become better
at math. To test the pill, a sample of 350 total students who failed the math placement
exam at PCC were selected and divided into 2 groups, a treatment group and a placebo
group. Each of the 350 students are supposed to take one pill everyday and take
PreAlgebra. The treatment group consists of 192 people and 134 of them passed
PreAlgebra. Of the 158 people in the placebo group, 97 passed PreAlgebra. Use a 0.05
significance level to determine if people who take this pill have a better chance of passing
PreAlgebra than those who don’t take the pill.
4. (30 points) In order to see if students gain weight in their first year in college, 8
random students were weighed once at the beginning of the fall semester and again at the
end of the Spring semester (weights are in lbs). The data is below. Use a 0.10
significance level to test the claim that freshmen gain weight during their first year of
college.
Weight at beginning of the Fall
Weight at end of the Spring
Ed
225
237
Sam
192
188
Jill
127
122
Joe
178
184
Fred
265
280
Mike
188
188
Jack
221
219
Jen
112
114
5. (30 points) Researchers conducted a study to determine whether magnets are effective
in treating back pain, with results given below. The values represent measurements of
pain using the visual analog scale. Use a 0.05 significance level to test the claim that
those given a sham treatment (similar to a placebo) have pain reductions that vary more
than the pain reductions for those treated with magnets.
Reduction in pain level after sham treatment: n  20 , x  0.44 , s  1.4
Reduction in pain level after magnet treatment: n  20 , x  0.49 , s  0.96