Statistics Exam - For each car entering the drive-through

Exam: 250712RR - Probability

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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. For each car entering the drive-through of a fast-food restaurant, x = the number of occupants. In this study, x is a

A. continuous quantitative variable.

B. joint probability.

C. dependent event.

D. discrete random variable.

 

2. 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. 4.2%

B. 2.1%

C. 4.5%

D. 0.3%

 

Protestant Catholic Jewish Other

Democrat 0.35 0.10 0.03 0.02

Republican 0.27 0.09 0.02 0.01

Independent 0.05 0.03 0.02 0.01

3. 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. 0.62

C. 0.35

D. 0.89

 

4. 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?

Brown-haired Blond

Short-haired 0.06 0.23

Shaggy 0.51 0.20

A. 0.0306

B. 0.105

C. 0.222

D. 0.06

 

5. Tornadoes for January in Kansas average 3.2 per month. What is the probability that, next January, Kansas will experience exactly two tornadoes? A. 0.1304

B. 0.2226

C. 0.4076

D. 0.2087

 

6. A new car salesperson knows that she sells a car to one customer out of 20 who enter the showroom. Find the probability that she'll sell a car to exactly two of the next three customers.

A. 0.1354

B. 0.0071

C. 0.0075

D. 0.9939

 

7. What is the value of ? A. 6720

B. 56

C. 1.6

D. 336

 

8. 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. 95.5%

B. 68.3%

C. 50%

D. 99.7%

 

9. The probability of an offender having a speeding ticket is 35%, having a parking ticket is 44%, having both is 12%. What is the probability of an offender having either a speeding ticket or a parking ticket or both? A. 67%

B. 55%

C. 91%

D. 79%

 

10. Each football game begins with a coin toss in the presence of the captains from the two opposing teams. (The winner of the toss has the choice of goals or of kicking or receiving the first kickoff.) A particular football team is scheduled to play 10 games this season. Let x = the number of coin tosses that the team captain wins during the season. Using the appropriate table in your textbook, solve for P(4 ≤ x ≤  8).

A. 0.246

B. 0.171

C. 0.377

D. 0.817

 

11. If event A and event B are mutually exclusive, P(A or B) = A. P(A) + P(B) – P(A and B).

B. P(A) + P(B).

C. P(A) – P(B).

D. P(A + B).

 

12. 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. 0

B. 22

C. 28

D. 10

 

13. 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. 0.80

B. 0.40

C. 0.20

D. 0.50

 

14. Which of the following is correct concerning the Poisson distribution?

A. The mean is usually smaller than the variance.

B. Each event being studied must be statistically dependent on the previous event.

C. The mean is usually larger than the variance.

D. The event being studied is restricted to a given span of time, space, or distance.

 

15. Which of the following is a discrete random variable? A. The weight of football players in the NFL

B. The number of three-point shots completed in a college basketball game

C. The average daily consumption of water in a household

D. The time required to drive from Dallas to Denver

 

16. 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. 0.931

B. 0.9895

C. 0.965

D. 0.049

 

17. 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. Events A and B are mutually exclusive.

B. On a Venn diagram, event B would contain event A.

C. Events A and B are exhaustive.

D. On a Venn diagram, event A would overlap event B.

 

18. Using the standard normal table in the textbook, determine the solution for P(0.00 ≤ z ≤ 2.01). A. 0.0222

B. 0.1179

C. 0.4821

D. 0.4778

 

19. 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. 68.3%

D. 94.8%

 

20. In the binomial probability distribution, p stands for the

End of exam

A. probability of failure in any given trial.

B. number of trials.

C. probability of success in any given trial.

D. number of successes.