Questions 1 to 20: Select the best answer to each question. Note that a question and its answers may be split across a page break, so be sure that you have seen the entire question and all the answers before choosing an answer.
1. Approximately how much of the total area under the normal curve will be in the interval spanning 2 standard deviations on either side of the mean?
A. 50%
B. 68.3%
C. 95.5%
D. 99.7%
2. A credit card company decides to study the frequency with which its cardholders charge for items from a certain chain of retail stores. The data values collected in the study appear to be normally distributed with a mean of 25 charged purchases and a standard deviation of 2 charged purchases. Out of the total number of cardholders, about how many would you expect are charging 27 or more purchases in this study?
A. 15.9%
B. 47.8%
C. 94.8%
D. 68.3%
3. A breeder records probabilities for two variables in a population of animals using the two-way table given here. Given that an animal is brown-haired, what is the probability that it's short-haired?
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Brown-haired Blond
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Short-haired
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0.06
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0.23
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Shaggy
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0.51
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0.20
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A. 0.0306
B. 0.105
C. 0.06
D. 0.222
4. Consider an experiment that results in a positive outcome with probability 0.38 and a negative outcome with probability 0.62. Create a new experiment consisting of repeating the original experiment 3 times. Assume each repetition is independent of the others. What is the probability of three successes?
A. 0.238
B. 0.762
C. 1.14
D. 0.055
5. An apartment complex has two activating devices in each fire detector. One is smoke-activated and has a probability of .98 of sounding an alarm when it should. The second is a heat-sensitive activator and has a probability of .95 of operating when it should. Each activator operates independently of the other. Presume a fire starts near a detector. What is the probability that both activating devices will work properly?
A. 0.9895
B. 0.049
C. 0.931
D. 0.965
6. If the mean number of hours of television watched by teenagers per week is 12 with a standard deviation of 2 hours, what proportion of teenagers watch 16 to 18 hours of TV a week? (Assume a normal distribution.)
A. 4.5%
B. 2.1%
C. 4.2%
D. 0.3%
7. Assume that an event A contains 10 observations and event B contains 15 observations. If the intersection of events A and B contains exactly 3 observations, how many observations are in the union of these two events?
A. 28
B. 0
C. 10
D. 22
8. A breeder records probabilities for two variables in a population of animals using the two-way table given here. Let A be the event "shaggy and brown-haired." Compute P(Ac).
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Brown-haired Blond
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Short-haired
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0.06
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0.23
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Shaggy
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0.51
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0.20
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A. 0.49
B. 0.77
C. 0.36
D. 0.51
9. If the probability that an event will happen is 0.3, what is the probability of the event's complement?
A. 0.3
B. 0.1
C. 1.0
D. 0.7
10. From an ordinary deck of 52 playing cards, one is selected at random. What is the probability that the selected card is either an ace, a queen, or a three?
A. 0.0769
B. 0.25
C. 0.2308
D. 0.3
11. Let event A = rolling a 1 on a die, and let event B = rolling an even number on a die. Which of the following is correct concerning these two events?
A. On a Venn diagram, event B would contain event A.
B. Events A and B are mutually exclusive.
C. On a Venn diagram, event A would overlap event B.
D. Events A and B are exhaustive.
12. A basketball team at a university is composed of ten players. The team is made up of players who play the position of either guard, forward, or center. Four of the ten are guards, four are forwards, and two are centers. The numbers that the players wear on their shirts are 1, 2, 3, and 4 for the guards; 5, 6, 7, and 8 for the forwards; and 9 and 10 for the centers. The starting five are numbered 1, 3, 5, 7, and 9. Let a player be selected at random from the ten. The events are defined as follows:
Let A be the event that the player selected has a number from 1 to 8. Let B be the event that the player selected is a guard.
Let C be the event that the player selected is a forward. Let D be the event that the player selected is a starter. Let E be the event that the player selected is a center.
Calculate P(C).
A. 0.50
B. 0.40
C. 0.80
D. 0.20
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Protestant Catholic Jewish Other
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Democrat
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0.35
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0.10
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0.03
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0.02
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Republican
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0.27
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0.09
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0.02
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0.01
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Independent
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0.05
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0.03
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0.02
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0.01
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13. The table above gives the probabilities of combinations of religion and political parties in a city in the United States. What is the probability that a randomly selected person will be a Protestant and at the same time be a Democrat or a Republican?
A. 0.67
B. 0.35
C. 0.62
D. 0.89
14. WHhat is the value of 8/5?
A. 56 B. 1.6 C. 6720 D. 336
15. In the binomial probability distribution, p stands for the
A. number of trials.
B. probability of failure in any given trial.
C. probability of success in any given trial.
D. number of successes.
16. The Burger Bin fast-food restaurant sells a mean of 24 burgers an hour and its burger sales are normally distributed. The standard deviation is 6. What is the probability that the Burger Bin will sell 12 to 18 burgers in an hour?
A. 0.136
B. 0.342
C. 0.475
D. 0.239
17. For each car entering the drive-through of a fast-food restaurant, x = the number of occupants. In this study, x is a
A. discrete random variable.
B. dependent event.
C. continuous quantitative variable.
D. joint probability.
18. Using the standard normal table in the textbook, determine the solution for P(0.00 ≤ z ≤ 2.01).
A. 0.0222
B. 0.4778
C. 0.1179
D. 0.4821
19. The area under the normal curve extending to the right from the midpoint to z is 0.17. Using the standard normal table on the textbook's back endsheet, identify the relevant z value.
A. 0.0675
B. 0.44
C. -0.0675
D. 0.4554
20. Tornadoes for January in Kansas average 3.2 per month. What is the probability that, next January, Kansas will experience exactly two tornadoes?
A. 0.2087
B. 0.2226
C. 0.4076
D. 0.1304