Download Solutions

Name: ________________________ Class: ___________________ Date: __________
ID: A
Ch 5 to 7 MC Practice
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. I select two cards from a deck of 52 cards and observe the color of each (26 cards in the deck are red and 26
are black). Which of the following is an appropriate sample space S for the possible outcomes?
A. S = {red, black}
B. S = {(red, red), (red, black), (black, red), (black, black)}, where, for example, (red, red)
stands for the event "the first card is red and the second card is red."
C. S = {(red, red), (red, black), (black, black)}, where, for example, (red, red) stands for the
event "the first card is red and the second card is red."
D. S = {0, 1, 2}.
E. All of the above.
____
2. An assignment of probabilities must obey which of the following?
A. The probability of any event must be a number between 0 and 1, inclusive.
B. The sum of all the probabilities of all outcomes in the sample space must be exactly 1.
C. The probability of an event is the sum of the probabilities of outcomes in the sample
space in which the event occurs.
D. All three of the above.
E. A and B only.
Scenario 5-2
If you draw an M&M candy at random from a bag of the candies, the candy you draw will have one of six
colors. The probability of drawing each color depends on the proportion of each color among all candies
made. The table below gives the probability that a randomly chosen M&M had each color before blue M &
M’s replaced tan in 1995.
Color
Probability
Brown
0.3
Red
0.2
Yellow
?
Green
0.1
____
3. Use Scenario 5-2. The probability of drawing a yellow candy is
A. 0.
B. .1.
C. .2.
D. .3.
E. impossible to determine from the information given.
____
4. Use Scenario 5-2. The probability that you do not draw a red candy is
A. .2.
B. .3.
C. .7.
D. .8.
E. impossible to determine from the information given.
1
Orange
0.1
Tan
0.1
Name: ________________________
ID: A
____
5. Use Scenario 5-2. The probability that you draw either a brown or a green candy is
A. .1.
B. .3.
C. .4.
D. .6.
E. .7.
____
6. Students at University X must have one of four class ranks—freshman, sophomore, junior, or senior. At
University X, 35% of the students are freshmen and 30% are sophomores. If a University X student is selected
at random, the probability that he or she is either a junior or a senior is
A. 30%.
B. 35%.
C. 65%.
D. 70%.
E. 89.5%.
Scenario 5-4
In a particular game, a fair die is tossed. If the number of spots showing is either four or five, you win $1. If
the number of spots showing is six, you win $4. And if the number of spots showing is one, two, or three, you
win nothing. You are going to play the game twice.
____
7. Use Scenario 5-4. The probability that you win $4 both times is
A. 1/36.
B. 1/12
C. 1/6.
D. 1/4.
E. 1/3.
____
8. Use Scenario 5-4. The probability that you win at least $1 both times is
A. 1/36.
B. 4/36.
C. 1/4.
D. 1/2.
E. 3/4.
2
Name: ________________________
ID: A
Scenario 5-13
One hundred high school students were asked if they had a dog, a cat, or both at home. Here are the results.
Dog?
Total
No
Yes
Cat?
No
74
4
78
Yes
10
12
22
Total
84
16
100
____
9. Use Scenario 5-13. If a single student is selected at random and you know she has a dog, what is the
probability she also has a cat?
A. 0.04
B. 0.12
C. 0.22
D. 0.25
E. 0.75
____ 10. Use Scenario 5-13. If a single student is selected at random, what is the probability associated with the union
of the events “has a dog” and “does not have a cat?”
A. 0.04
B. 0.16
C. 0.78
D. 0.9
E. 0.94
____ 11. Use Scenario 5-13. If two students are selected at random, what is the probability that neither of them has a
dog or a cat?
A. 0.37
B. 0. 540
C. 0. 548
D. 0.655
E. 0.74
____ 12. Which of the following is not a random variable?
A. The heights of randomly-selected buildings in New York City.
B. The suit of a card randomly-selected from a 52-card deck.
C. The number of children in randomly-selected households in the United States.
D. The amount of money won (or lost) by the next person to walk out of a casino in Las
Vegas.
E. All of the above are random variables.
____ 13. Which of the following is true about every random variable
I. It takes on numerical or categorical values.
II. It describes the results of a random phenomenon.
III. Its behavior can be described by a probability distribution.
A. I only
B. II only
C. III only
D. II and III
E. All three statements are true
3
Name: ________________________
ID: A
Scenario 6-2
In a particular game, a fair die is tossed. If the number of spots showing is either 4 or 5 you win $1, if the
number of spots showing is 6 you win $4, and if the number of spots showing is 1, 2, or 3 you win nothing.
Let X be the amount that you win.
____ 14. Use Scenario 6-2. Which of the following is the expected value of X?
A. $0.00
B. $1.00
C. $2.50
D. $4.00
E. $6.00
____ 15. Use Scenario 6-2. Which of the following is the standard deviation of X?
A. $1.00
B. $1.35
C. $1.41
D. $1.78
E. $2.00
Scenario 6-4
Number of cards
10
1000
5000
Payoff
$1,000
$50
$5
In the Florida scratch-card lottery, the numbers and values of prizes awarded for every 100,000 cards sold are
____ 16. Use Scenario 6-4. The probability that a random scratch-card will pay off is
A. .0250.
B. .0601.
C. .2500.
D. .6010.
E. .8500.
____ 17. Use Scenario 6-4. The expected payoff per card sold is
A. $1.00.
B. $.90.
C. $.85.
D. $.50.
E. $.25.
4
Name: ________________________
ID: A
Scenario 6-10
Your friend Albert has invented a game involving two ten-sided dice. One of the dice has threes, fours, and
fives on its faces, the other has sixes, eights, and tens. He won’t tell you how many of each number there are
on the faces, but he does tell you that if X = rolls of the first die and Y = rolls of the second die, then
Let Z = the sum of the two dice when each is rolled once.
____ 18. Use Scenario 6-10. What is the expected value of Z?
A. 1.7
B. 4.4
C. 8.8
D. 8.9
E. 11.6
____ 19. Use Scenario 6-10. What is the standard deviation of Z?
A. 1.20
B. 1.30
C. 1.45
D. 1.70
E. 2.89
____ 20. Use Scenario 6-10. Here’s Albert’s game: You give him $10 each time you roll, and he pays you (in dollars)
the amount that comes up on the dice. If P = the amount of money you gain each time you roll, the mean and
standard deviation of P are:
A.
B.
C.
D.
E.
____ 21. Sulé’s job is just a few bus stops away from his house. While it can be faster to take the bus to work, it’s
more variable, because of variations in traffic. He estimates that the commute time to work by bus is
approximately Normally distributed with a mean of 12 minutes and a standard deviation of 4 minutes. The
commute time if he walks to work is also approximately Normally distributed with a mean of 16 minutes with
a standard deviation of 1 minute. What is the probability that the bus will be faster than walking?
A. 0.8340
B. 0.8485
C. 0.8980
D. 0.9756
E. 0.9896
____ 22. An airplane has a front and a rear door that are both opened to allow passengers to exit when the plane lands.
The plane has 100 passengers seated. The number of passengers exiting through the front door should have
A. a binomial distribution with mean 50.
B. a binomial distribution with 100 trials but success probability not equal to 0.5.
C. a geometric distribution with p = 0.5.
D. a normal distribution with a standard deviation of 5.
E. none of the above.
5
Name: ________________________
ID: A
Scenario 6-12
There are twenty multiple-choice questions on an exam, each having responses a, b, c, or d. Each question is
worth five points and only one option per question is correct. Suppose the student guesses the answer to each
question, and the guesses from question to question are independent.
____ 23. Use Scenario 6-12. Which of the following expresses the probability that the student gets no questions
correct?
A.
B.
C.
D.
E.
Scenario 6-13
A survey asks a random sample of 1500 adults in Ohio if they support an increase in the state sales tax from
5% to 6%, with the additional revenue going to education. Let X denote the number in the sample that say
they support the increase. Suppose that 40% of all adults in Ohio support the increase.
____ 24. Use Scenario 6-13. Which of the following is the mean  of X?
A. 5%
B. 360
C. 0.40
D. 600
E. 90
____ 25. Use Scenario 6-13. Which of the following is the approximate standard deviation  of X ?
A. 0.40
B. 0.24
C. 19
D. 360
E. 9.20
____ 26. In the 2008 New Hampshire Democratic primary, 30% of voter in a CNN poll said they would vote for
Hillary Clinton. Surprisingly, in the primary itself, 39% voted for Clinton. The number 39% is a
A. parameter.
B. population.
C. statistic.
D. sample.
E. sampling distribution.
6
Name: ________________________
ID: A
Scenario 7-1
A CBS News/New York Times opinion poll asked 1,190 adults whether they would prefer balancing the
Federal budget over cutting taxes; 59% of those asked said "Yes." Suppose that in fact 62% of all adults
favor balancing the budget over cutting taxes.
____ 27. Use Scenario 7-1. The number 62%
A. is evidence of bias.
B. must be an error, since the actual percentage is 59%.
C. is a sampling distribution.
D. is a statistic.
E. is a parameter.
____ 28. Use Scenario 7-1. If you take a large number of SRSs of size 1,190, the sample proportions who favor
balancing the budget will vary. Some will be lower than 62% and some will be higher, but the average sample
result will be very close to 62%. This fact is called
A. low bias.
B. small margin of error.
C. high variability.
D. large bias.
E. low variability.
Scenario 7-2
Below are dot plots of the values taken by three different statistics in 30 samples from the same population.
The true value of the population parameter is marked with an arrow.
____ 29. Use Scenario 7-2. The statistic that has the largest bias among these three is
A. statistic A.
B. statistic B.
C. statistic C.
D. A and B have similar bias, and it is larger than the bias of C.
E. B and C have similar bias, and it is larger than the bias of A.
____ 30. Use Scenario 7-2. The statistic that has the lowest variability among these three is
A. statistic A.
B. statistic B.
C. statistic C.
D. A and B have similar variability, and it is less than the variability of C.
E. B and C have similar variability, and it is less than the variability of A.
7
Name: ________________________
ID: A
____ 31. Use Scenario 7-2. Based on the performance of the three statistics in many samples, which is preferred as an
estimate of the parameter?
A. statistic A.
B. statistic B.
C. statistic C.
D. either A or B would be equally good.
E. either B or C would be equally good.
____ 32. If we took a SRS of 1700 people from California (population 34 million) and a SRS of 1000 people from
Detroit (population 1 million) which sampling distribution would have the smaller standard deviation?
A. Detroit, because 1000/1,000,000 is more than 1700/32,000,000.
B. Detroit, because it has the smaller population.
C. California, because the sample size (1700) is larger than for Detroit (1000).
D. California, because it has the larger population.
E. Both would be the same, because simple random samples (SRS) are taken in both places.
Scenario 7-4
According to a recent poll, 27% of Americans get 30 minutes of exercise at least five days each week. Let’s
assume this is the parameter value for the population.
____ 33. Use Scenario 7-4. If you take a simple random sample of 25 Americans and let = the proportion in the
sample who get 30 minutes of exercise at least fives days per week, what are the mean and standard deviation
of the sampling distribution of ?
A.
B.
C.
D.
E.
____ 34. Use Scenario 7-4. If you take a simple random sample of 25 Americans and let = the proportion in the
sample who get 30 minutes of exercise at least fives days per week, is the shape of the sampling distribution
of approximately Normal?
A. No, because
B. No, because
C. Yes, because we can reasonably assume that there are more than
individuals in the population.
D. Yes, because we took a simple random sample.
.
E. Yes, because
8
Name: ________________________
ID: A
____ 35. Use Scenario 7-4. Suppose you increased the sample size in the previous question to
. How would the
?
sampling distribution of compare to the sampling distribution for
A. Center and spread would be the same, both distributions would be approximately Normal.
B. Center and spread would be the same, but only the shape for the larger sample would be
approximately Normal.
C. Center would be the same, spread would be smaller for
, both distributions would
be approximately Normal.
, and only the shape for
D. Center would be the same, spread would be smaller for
the larger sample would be approximately Normal.
, and only the shape for the
E. Center would be the same, spread would be larger for
larger sample would be approximately Normal.
were taken, what is the approximate probability that
____ 36. Use Scenario 7-4. If an SRS of size
proportion who exercise at least five days per week, is higher than 0.30?
A. nearly 0.
B. 0.1081
C. 0.1163
D. 0.1227
E. 0.3164
, the
____ 37. A fair coin (one for which both the probability of heads and the probability of tails are 0.5) is tossed 60 times.
The probability that less than 1/3 of the tosses are heads is closest to
A. 0.9951.
B. 0.33.
C. 0.109.
D. 0.09.
E. 0.0049.
____ 38. A college basketball player makes 80% of his free throws. Over the course of the season she will attempt 100
free throws. Assuming free throw attempts are independent, the probability that the number of free throws she
makes exceeds 80 is approximately
A. 0.2000.
B. 0.2266.
C. 0.5000.
D. 0.7734.
E. 0.8000.
____ 39. The distribution of prices for home sales in a certain New Jersey county is skewed to the right with a mean of
$290,000 and a standard deviation of $145,000. Suppose you take a simple random sample of 100 home
sales from this (very large) population. What is the probability that the mean of our sample is above
$325,000?
A. 0.0015
B. 0.0027
C. 0.0079
D. 0.4046
E. 0.4921
9
ID: A
Ch 5 to 7 MC Practice
Answer Section
MULTIPLE CHOICE
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
33.
34.
35.
36.
37.
38.
39.
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
TOP:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
B
PTS: 1
TOP: Sample space
D
PTS: 1
TOP: Basic Probability Rules
C
PTS: 1
TOP: Basic Probability Rules
D
PTS: 1
TOP: Complement rule
C
PTS: 1
TOP: Addition of disjoint events
B
PTS: 1
TOP: Addition of disjoint events
A
PTS: 1
TOP: Multiplication Rule, Independent events
C
PTS: 1
TOP: Multiplication Rule, Independent events; Complement
E
PTS: 1
TOP: Conditional probability from 2-way table
D
PTS: 1
TOP: Conditional probability from 2-way table
C
PTS: 1
TOP: Conditional probability from 2-way table
B
PTS: 1
TOP: Identifying random variables
D
PTS: 1
TOP: Idea of random variable
B
PTS: 1
TOP: Mean of Discrete Random Variable
C
PTS: 1
TOP: Standard deviation of Discrete R.V.
B
PTS: 1
TOP: Discrete random variables: probabilities from tables
C
PTS: 1
TOP: Mean of Discrete Random Variable
E
PTS: 1
TOP: Mean of sum of random variables
A
PTS: 1
TOP: Std. dev. of sum of random variables
C
PTS: 1
TOP: Linear transformation of random variable
A
PTS: 1
TOP: Combining normal random variables
E
PTS: 1
TOP: Binomial/Geometric setting
B
PTS: 1
TOP: Binomial probability
D
PTS: 1
TOP: Binomial mean
C
PTS: 1
TOP: Binomial standard deviation
A
PTS: 1
TOP: Parameter vs. Statistic
E
PTS: 1
TOP: Parameter vs. Statistic
A
PTS: 1
TOP: Bias and variability
C
PTS: 1
TOP: Bias and variability
E
PTS: 1
TOP: Bias and variability
B
PTS: 1
TOP: Bias and variability
C
PTS: 1
TOP: Variability and sample size
D
PTS: 1
Mean and Std. Dev. of sampling distribution of proportions
B
PTS: 1
TOP: Normality condition
D
PTS: 1
TOP: Normal probability calculation for p-hat
E
PTS: 1
TOP: Normal probability calculation for p-hat
E
PTS: 1
TOP: Normal probability calculation for p-hat
C
PTS: 1
TOP: Normal probability calculation for p-hat
C
PTS: 1
TOP: Normal probability calculation for sampl. distrib. of x-bar
1