Assignment- Probability

1. 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. 94.8%
B. 15.9%
C. 68.3%
D. 47.8%

2. 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).

A. 0.51
B. 0.49
C. 0.77
D. 0.36

3. Find the z-score that determines that the area to the right of z is 0.8264.
A. -0.94
B. -1.36
C. 0.94
D. 1.36

4. 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

5. 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. 0.3%
C. 4.5%
D. 2.1%

6. If event A and event B are mutually exclusive, P(A or B) =
A. P(A + B).
B. P(A) + P(B).
C. P(A) + P(B) - P(A and B).
D. P(A) - P(B).

7. 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. 0.055
B. 1.14
C. 0.238
D. 0.762

8. In the binomial probability distribution, p stands for the
A. number of trials.
B. probability of success in any given trial.
C. number of successes.
D. probability of failure in any given trial.

9. Using the standard normal table in the textbook, determine the solution for P(0.00 ≤ z ≤ 2.01).
A. 0.4821
B. 0.0222
C. 0.4778
D. 0.1179

10. The possible values of x in a certain continuous probability distribution consist of the infinite number of values between 1 and 20. Solve for P(x = 4).
A. 0.00
B. 0.05
C. 0.03
D. 0.02

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 exhaustive.
C. Events A and B are mutually exclusive.
D. On a Venn diagram, event A would overlap event B.

12. 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. 0.2308
B. 0.0769
C. 0.25
D. 0.3

13. 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?

A. 0.105
B. 0.222
C. 0.0306
D. 0.06

14. 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. 0.80
C. 0.20
D. 0.40

15. 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. 55%
B. 67%
C. 91%
D. 79%

16. 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. dependent event.
C. joint probability.
D. discrete random variable.

17. 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. 0.9939
B. 0.1354
C. 0.0071
D. 0.0075

18. A continuous probability distribution represents a random variable
A. having an infinite number of outcomes that may assume any number of values within an interval.
B. having outcomes that occur in counting numbers.
C. that has a definite probability for the occurrence of a given integer.
D. that's best described in a histogram.

19. The Burger Bin fast-food restaurant sells a mean of 24 burgers an hour and its burger sales are normally distributed. If hourly sales fall between 24 and 42 burgers 49.85% of the time, the standard deviation is burgers.
A. 3
B. 6
C. 18
D. 9

20. 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. 0.171
B. 0.377
C. 0.246
D. 0.817