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 pagebreak, so be sure that you have seen the entire question and all the answers before choosing an answer.
1. A breeder records probabilities for two variables in a population of animals using the two-way table givenhere. Given that an animal is brown-haired, what is the probability that it’s short-haired?
Short-haired 0.06 0.23
Shaggy 0.51 0.20
2. 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 particularfootball team is scheduled to play 10 games this season. Let x = the number of coin tosses that the teamcaptain wins during the season. Using the appropriate table in your textbook, solve for P(4 ≤ x ≤ 8).
3. If the mean number of hours of television watched by teenagers per week is 12 with a standard deviationof 2 hours, what proportion of teenagers watch 16 to 18 hours of TV a week? (Assume a normaldistribution.)
4. 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).
5. Find the z-score that determines that the area to the right of z is 0.8264.
6. The Burger Bin fast-food restaurant sells a mean of 24 burgers an hour and its burger sales are normallydistributed. If hourly sales fall between 24 and 42 burgers 49.85% of the time, the standard deviation is_______ burgers.
7. Using the standard normal table in the textbook, determine the solution for P(0.00 ≤ z ≤ 2.01).
8. Which of the following is correct concerning the Poisson distribution?
A. The mean is usually smaller than the variance.
B. The mean is usually larger than the variance.
C. Each event being studied must be statistically dependent on the previous event.
D. The event being studied is restricted to a given span of time, space, or distance.
9. A breeder records probabilities for two variables in a population of animals using the two-way table givenhere. Let A be the event “shaggy and brown-haired.” Compute P(Ac).
Short-haired 0.06 0.23
Shaggy 0.51 0.20
10. If the probability that an event will happen is 0.3, what is the probability of the event’s complement?
11. 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.
12. For each car entering the drive-through of a fast-food restaurant, x = the number of occupants. In thisstudy, x is a
A. discrete random variable.
B. dependent event.
C. continuous quantitative variable.
D. joint probability.
13. Assume that an event A contains 10 observations and event B contains 15 observations. If theintersection of events A and B contains exactly 3 observations, how many observations are in the union ofthese two events?
14. Let event A = rolling a 1 on a die, and let event B = rolling an even number on a die. Which of thefollowing is correct concerning these two events?
A. Events A and B are mutually exclusive.
B. On a Venn diagram, event A would overlap event B.
C. Events A and B are exhaustive.
D. On a Venn diagram, event B would contain event A.
15. The possible values of x in a certain continuous probability distribution consist of the infinite number ofvalues between 1 and 20. Solve for P(x = 4).
16. A credit card company decides to study the frequency with which its cardholders charge for items froma certain chain of retail stores. The data values collected in the study appear to be normally distributed witha mean of 25 charged purchases and a standard deviation of 2 charged purchases. Out of the total numberof cardholders, about how many would you expect are charging 27 or more purchases in this study?
17. The probability of an offender having a speeding ticket is 35%, having a parking ticket is 44%, havingboth is 12%. What is the probability of an offender having either a speeding ticket or a parking ticket orboth?
18. From an ordinary deck of 52 playing cards, one is selected at random. What is the probability that theselected card is either an ace, a queen, or a three?
19. Consider an experiment that results in a positive outcome with probability 0.38 and a negative outcomewith 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?
20. An apartment complex has two activating devices in each fire detector. One is smoke-activated and hasa probability of .98 of sounding an alarm when it should. The second is a heat-sensitive activator and has aprobability of .95 of operating when it should. Each activator operates independently of the other. Presumea fire starts near a detector. What is the probability that both activating devices will work properly?