# Solve problems involving the Poisson distribution using the Poisson formula and the Poisson table

Chapter 5: Discrete Distributions

True/False

1. Variables which take on values only at certain points over a given interval are called continuous random variables

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.

2. A variable that can take on values at any point over a given interval is called a discrete random variable

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.

3. The number of visitors to a website each day is an example of a discrete random variable

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.

4. The amount of time a patient waits in a doctor’s office is an example of a continuous random variable

Ans:

Response: See section 5.1 Discrete versus Continuous Distributions

Difficulty: Easy

5. The mean or the expected value of a discrete distribution is the long-run average of the occurrences.

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.

6. To compute the variance of a discrete distribution, it is not necessary to know the mean of the distribution.

Ans:

Response: See section 5.2 Describing a Discrete Distribution

Difficulty: Medium

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

7. The variance of a discrete distribution increases if we add a positive constant to each one of its value.

Ans:

Response: See section 5.2 Describing a Discrete Distribution

Difficulty: Medium

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

8. In a binomial experiment, any single trial contains only two possible outcomes and successive trials are independent.

Ans:

Response: See section 5.3 Binomial Distribution

Difficulty: Medium

Learning Objective: 5.3: Solve problems involving the binomial distribution using the binomial formula and the binomial table.

9. In a binomial distribution, p, the probability of getting a successful outcome on any single trial, increases proportionately with every success.

Ans:

Response: See section 5.3 Binomial Distribution

Difficulty: Medium

Learning Objective: 5.3: Solve problems involving the binomial distribution using the binomial formula and the binomial table.

10. The assumption of independent trials in a binomial distribution is not a great concern if the sample size is smaller than 1/20th of the population size.

Ans:

Response: See section 5.3 Binomial Distribution

Difficulty: Medium

Learning Objective: 5.3: Solve problems involving the binomial distribution using the binomial formula and the binomial table.

11. For a binomial distribution in which the probability of success is p = 0.5, the variance is twice the mean.

Ans:

Response: See section 5.3 Binomial Distribution

Difficulty: Hard

12. The Poisson distribution is a continuous distribution which is very useful in solving waiting time problems

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.

13. Both the Poisson and the binomial distributions are discrete distributions and both have a given number of trials.

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.

14. The Poisson distribution is best suited to describe occurrences of rare events in a situation where each occurrence is independent of the other occurrences.

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.

15. For the Poisson distribution the mean represents twice the value of the standard deviation..

Ans:

Response: See section 5.4 Poisson Distribution

Difficulty: Easy