Student ID: 22144192

Exam: 350363RR – 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. Consider the Venn diagram shown, which contains five sample points. The probabilities assigned to each sample are as follows: P(E1) = .20, P(E2) = .30, P(E3) = .30, P(E4) = .10, P(E5) = .10

Find P(B) A. .3

B. 0

C. .5

D. .7

2. Compute how many ways you can select n elements from N elements when n = 2 and N = 5. A. 7

B. 25

C. 10

D. 12

3. To determine whether a piece of factory equipment is working properly, the floor manager performs a test run of 25 units. Each unit is measured, and the factory worker finds that the standard deviation in the measurements over a long period of time is .001. What’s the approximate probability that the mean measurement of the units from the test run will lie within .0001 of the mean unit measurement? A. .3830

B. .3953

C. .3542

D. .2750

4. Compute how many ways you can select n elements from N elements when n = 5 and N = 20. A. 15,504

B. 775

C. 225

D. 100

5. A racetrack accepts bets that consist of picking the first and second finisher, regardless of the order that the two racers finished. There are eight racers in each run. Suppose you pick a combination of two racers at random. Assuming that they all have an equal probability of winning, what’s your likelihood of winning your bet?

A. 1/16

B. 1/28

C. 1/4

D. 1/8

6. The Burger Bin 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. 9

B. 3

C. 18

D. 6

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. 0

B. 18

C. 10

D. 22

8. If x is a binomial random variable, find p(x) when n = <5, x = 1, and p = .2 A. .644

B. .027

C. .1611

D. .4096

9. The Internal Revenue Service (IRS) audited 1,242,479 individual tax returns in the year 2013. A total of 145,236,429 individuals filed tax returns that year. Also in 2013, the IRS audited 25,905 corporate tax returns out of a total 1,924,887 filed. Assume that returns are selected for audits at random. What’s the probability a randomly-selected corporate tax return is audited?

A. .0135

B. .9865

C. .0086

D. .9914

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

B. P(A + B).

C. P(A) + P(B) – P(A and B).

D. P(A) – P(B).

11. You take a random sample of n = 900 observations from a population with a mean of 100 and a standard deviation of 10. What’s the largest value of x you would expect to find? A. 108

B. 101

C. 100

D. 110

12. A basketball team at a university is composed of 10 players. The team is made up of players who play the position of either guard, forward, or center. Four of the 10 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 10. 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. 0.50

C. 0.40

D. 0.20

13. A continuous probability distribution represents a random variable A. having outcomes that occur in counting numbers.

B. that has a definite probability for the occurrence of a given integer.

C. that’s best described in a histogram.

D. having an infinite number of outcomes that may assume any number of values within an interval.

14. 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 end sheet, identify the relevant z value. A. 0.44

C. -0.0675

D. 3,600

E. 0.255

F. 1,800

15. 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. 0.759

B. 0.191

C. 0.815

D. 0.817

16. Assume x is a normally distributed random variable with mean = 11 and variance = 2. Find P(6 ≤ x ≤  10). A. 0

B. .1525

C. .3830

D. .3023

17. Approximately how much of the total area under the normal curve will be in the interval spanning two standard deviations on either side of the mean? A. 68.3%

B. 95.5%

C. 99.7%

D. 50%

18. You take a random sample of n = 900 observations from a population with a mean of 100 and a standard deviation of 10. What’s the smallest value of x you would expect to find? A. 99

B. 96

C. 101

D. 100

19. Assume x is a normally distributed random variable with mean = 50 and variance = 3. Find the value of

End of exam

the random variable x0 when P(x ≤ x0) = .8413

A. 49

B. 16

C. 33

D. 53

20. According to driver safety statistics in a particular area, one percent of drivers reported that they never wear their seatbelts. If five drivers in the area were randomly selected, what’s the probability that one would not be wearing a seatbelt? A. .001

B. .8116

C. .052

D. .048