# Discrete Distributions

Chapter 5: Discrete Distributions

16. A binomial distribution is better than a Poisson distribution to describe the occurrence of major oil spills in the Gulf of Mexico.

Ans:

Response: See section 5.4 Poisson Distribution

Difficulty: Medium

Learning Objective: 5.4: Solve problems involving the Poisson distribution using the Poisson formula and the Poisson table.

17. For the Poisson distribution the mean and the variance are the same.

Ans:

Response: See section 5.4 Poisson Distribution

Difficulty: Easy

Learning Objective: 5.4: Solve problems involving the Poisson distribution using the Poisson formula and the Poisson table.

18. Poisson distribution describes the occurrence of discrete events that may occur over a continuous interval of time or space.

Ans:

Response: See section 5.4 Poisson Distribution

Difficulty: Hard

Learning Objective: 5.4: Solve problems involving the Poisson distribution using the Poisson formula and the Poisson table.

19. A Poisson distribution is characterized by one parameter.

Ans:

Response: See section 5.4 Poisson Distribution

Difficulty: Medium

Learning Objective: 5.4: Solve problems involving the Poisson distribution using the Poisson formula and the Poisson table.

20. A hypergeometric distribution applies to experiments in which the trials represent sampling with replacement.

Ans:

Response: See section 5.5 Hypergeometric Distribution

Difficulty: Easy

Learning Objective: 5.5: Solve problems involving the hypergeometric distribution using the hypergeometric formula.

21. As in a binomial distribution, each trial of a hypergeometric distribution results in one of two mutually exclusive outcomes, i.e., either a success or a failure.

Ans:

Response: See section 5.5 Hypergeometric Distribution

Difficulty: Medium

Learning Objective: 5.5: Solve problems involving the hypergeometric distribution using the hypergeometric formula.

22. The number of successes in a hypergeometric distribution is unknown

Ans:

Response: See section 5.5 Hypergeometric Distribution

Difficulty: Hard

Learning Objective: 5.5: Solve problems involving the hypergeometric distribution using the hypergeometric formula.

23. In a hypergeometric distribution the population, N, is finite and known.

Ans:

Response: See section 5.5 Hypergeometric Distribution

Difficulty: Hard

Learning Objective: 5.5: Solve problems involving the hypergeometric distribution using the hypergeometric formula.

Multiple Choice

24.          The volume of liquid in an unopened 1-gallon can of paint is an example of _________.

a) the binomial distribution

b) both discrete and continuous variable

c) a continuous random variable

d) a discrete random variable

e) a constant

Ans:

Response: See section 5.1 Discrete versus Continuous Distributions

Difficulty: Medium

Learning Objective: 5.1: Define a random variable in order to differentiate between a discrete distribution and a continuous distribution.

25.          The number of  finance majors within the School of Business is an example of _______.

a) a discrete random variable

b) a continuous random variable

c) the Poisson distribution

d) the normal distribution

e) a constant

Ans:

Response: See section 5.1 Discrete versus Continuous Distributions

Difficulty: Easy

Learning Objective: 5.1: Define a random variable in order to differentiate between a discrete distribution and a continuous distribution.

26. The speed at which a jet plane can fly is an example of _________.

a) neither discrete nor continuous random variable

b) both discrete and continuous random variable

c) a continuous random variable

d) a discrete random variable

e) a constant

Ans:

Response: See section 5.1 Discrete versus Continuous Distributions

Difficulty: Medium

Learning Objective: 5.1: Define a random variable in order to differentiate between a discrete distribution and a continuous distribution.

27. In American Roulette, there are two zeroes and 36 non-zero numbers (18 red and 18 black). If a player bets 1 unit on red, his chance of winning 1 unit is therefore 18/38 and his chance of losing 1 unit (or winning -1) is 20/38. Let x be the player profit per game. The mean (average) value of x is approximately_______________.

a) 0.0526

b) -0.0526

c) 1

d) -1

e) 0

Ans:

Response: See section 5.2 Describing a Discrete Distribution

Difficulty: Easy

Learning Objective: 5.2: Determine the mean, variance, and standard deviation of a discrete distribution.

28.          A recent analysis of the number of rainy days per month found the following outcomes and probabilities.

Number of Raining Days (x)         P(x)

3              .40

4              .20

5              .40

The mean of this distribution is _____________.

a) 2

b) 3

c) 4

d) 5

e) <1

Ans:

Response: See section 5.2 Describing a Discrete Distribution

Difficulty: Easy

Learning Objective: 5.2: Determine the mean, variance, and standard deviation of a discrete distribution.

29.

A recent analysis of the number of rainy days per month found the following outcomes and probabilities.

Number of Raining Days (x)         P(x)

3              .40

4              .20

5              .40

The standard deviation of this distribution is _____________.

a) .800

b) .894

c) .400

d) 4.00

e) .457

Ans:

Response: See section 5.2 Describing a Discrete Distribution

Difficulty: Easy

Learning Objective: 5.2: Determine the mean, variance, and standard deviation of a discrete distribution.

30.          You are offered an investment opportunity.  Its outcomes and probabilities are presented in the following table.

x              P(x)

-\$1,000 .40

\$0           .20

+\$1,000                .40

Which of the following statements is true?

a) This distribution is skewed to the right.

b) This is a binomial distribution.

c) This distribution is symmetric.

d) This distribution is skewed to the left.

e) This is a Poisson distribution

Ans:

Response: See section 5.2 Describing a Discrete Distribution

Difficulty: Easy

Learning Objective: 5.2: Determine the mean, variance, and standard deviation of a discrete distribution. [checkout]