Applied Statistics in Business and Economics 5th Edition by Doane TB

Applied Statistics in Business and Economics 5th Edition by Doane TB

Chapter 06
Discrete Probability Distributions

True / False Questions

1. A random variable is a function or rule that assigns a numerical value to each outcome in the sample space of a stochastic (chance) experiment.

True False

2. A discrete random variable has a countable number of distinct values.

True False

3. The expected value of a discrete random variable E(X) is the sum of all X values weighted by their respective probabilities.

True False

4. A discrete distribution can be described by its probability density function (PDF) or by its cumulative distribution function (CDF).

True False

5. A random variable may be discrete or continuous, but not both.

True False

6. To describe the number of blemishes per sheet of white bond paper, we would use a discrete uniform distribution.

True False

7. The outcomes for the sum of two dice can be described as a discrete uniform distribution.

True False

8. A discrete binomial distribution is skewed right when π > .50.

True False

9. When π = .70 the discrete binomial distribution is negatively skewed.

True False

10. The Poisson distribution describes the number of occurrences within a randomly chosen unit of time or space.

True False

11. The Poisson distribution can be skewed either left or right, depending on λ.

True False

12. Although the shape of the Poisson distribution is positively skewed, it becomes more nearly symmetric as its mean becomes larger.

True False

13. As a rule of thumb, the Poisson distribution can be used to approximate a binomial distribution when n ≥ 20 and π ≤ .05.

True False

14. The hypergeometric distribution is skewed right.

True False

15. The hypergeometric distribution assumes that the probability of a success remains the same from one trial to the next.

True False

16. The hypergeometric distribution is not applicable if sampling is done with replacement.

True False

17. As a rule of thumb, the binomial distribution can be used to approximate the hypergeometric distribution whenever the population is at least 20 times as large as the sample.

True False

18. An example of a geometric random variable is the number of pine trees with pine beetle infestation in a random sample of 15 pine trees in Colorado.

True False

19. Calculating the probability of getting three aces in a hand of five cards dealt from a deck of 52 cards would require the use of a hypergeometric distribution.

True False

20. The Poisson distribution is appropriate to describe the number of babies born in a small hospital on a given day.

True False

21. The gender (M, F) of a randomly chosen unborn child is a Bernoulli event.

True False

22. The Poisson distribution has only one parameter.

True False

23. The standard deviation of a Poisson random variable is the square root of its mean.

True False

24. Customer arrivals per unit of time would tend to follow a binomial distribution.

True False

25. The two outcomes (success, failure) in the Bernoulli model are equally likely.

True False

26. The expected value of a random variable is its mean.

True False

Multiple Choice Questions

27. A discrete probability distribution:

A. is a listing of all possible values of the random variable.

B. assigns a probability to each possible value of the random variable.

C. can assume values between -1 and +1.

D. is independent of the parameters of the distribution.

28. The number of male babies in a sample of 10 randomly chosen babies is a:

A. continuous random variable.

B. Poisson random variable.

C. binary random variable.

D. binomial random variable.

29. A discrete random variable:

A. can be treated as continuous when it has a large range of values.

B. cannot be treated as continuous.

C. is best avoided if at all possible.

D. is usually uniformly distributed.

30. Which is not a discrete random variable?

A. The number of defects in a 4 × 8 sheet of plywood

B. The number of female passengers who board a plane

C. The time until failure of a vehicle headlamp

D. The number of correct answers on a statistics exam

31. Which is not a discrete random variable?

A. The number of births in a hospital on a given day

B. The number of fives obtained in four rolls of a die

C. The hourly earnings of a call center employee in Boston

D. The number of applicants applying for a civil service job

32. Which statement is incorrect?

A. The Poisson distribution is always skewed right.

B. The binomial distribution may be skewed left or right.

C. The discrete uniform distribution is always symmetric.

D. The hypergeometric distribution is symmetric.

33. The random variable X is the number of shots it takes before you make the first free throw in basketball. Assuming the probability of success (making a free throw) is constant from trial to trial, what type of distribution does X follow?

A. Binomial

B. Poisson

C. Hypergeometric

D. Geometric

34. Which probability model is most nearly appropriate to describe the number of burned-out fluorescent tubes in a classroom with 12 fluorescent tubes, assuming a constant probability of a burned-out tube?

A. Binomial

B. Poisson

C. Hypergeometric

D. Geometric

35. Which distribution is most nearly appropriate to describe the number of fatalities in Texas in a given year due to poisonous snakebites?

A. Binomial

B. Poisson

C. Hypergeometric

D. Geometric

36. Which model would you use to describe the probability that a call-center operator will make the first sale on the third call, assuming a constant probability of making a sale?

A. Binomial

B. Poisson

C. Hypergeometric

D. Geometric

37. In a randomly chosen week, which probability model would you use to describe the number of accidents at the intersection of two streets?

A. Binomial

B. Poisson

C. Hypergeometric

D. Geometric

38. Which model best describes the number of nonworking web URLs (“This page cannot be displayed”) you encounter in a randomly chosen minute while surfing websites for Florida vacation rental condos?

A. Binomial

B. Poisson

C. Hypergeometric

D. Geometric

39. Which probability model would you use to describe the number of damaged printers in a random sample of 4 printers taken from a shipment of 28 printers that contains 3 damaged printers?

A. Poisson

B. Hypergeometric

C. Binomial

D. Uniform

40. Which model best describes the number of incorrect fare quotations by a well-trained airline ticket agent between 2 p.m. and 3 p.m. on a particular Thursday?

A. Binomial

B. Poisson

C. Hypergeometric

D. Geometric

41. Which model best describes the number of blemishes per sheet of white bond paper?

A. Binomial

B. Poisson

C. Hypergeometric

D. Geometric

42. To ensure quality, customer calls for airline fare quotations are monitored at random. On a particular Thursday afternoon, ticket agent Bob gives 40 fare quotations, of which 4 are incorrect. In a random sample of 8 of these customer calls, which model best describes the number of incorrect quotations Bob will make?

A. Binomial

B. Poisson

C. Hypergeometric

D. Geometric

43. The number of people injured in rafting expeditions on the Colorado River on a randomly chosen Thursday in August is best described by which model?

A. Binomial

B. Poisson

C. Hypergeometric

D. Geometric

44. On a particular Thursday in August, 40 Grand Canyon tourists enter a drawing for a free mule ride. Ten of the entrants are European tourists. Five entrants are selected at random to get the free mule ride. Which model best describes the number of European tourists in the random sample?

A. Binomial

B. Poisson

C. Hypergeometric

D. Geometric

45. Which model best describes the number of births in a hospital until the first twins are delivered?

A. Binomial

B. Poisson

C. Hypergeometric

D. Geometric