Question 1

Which of the following is a characteristic of a discrete random variable?

Accepted Answer

It has a finite or countable number of possible values.

Question 2

Which of the following is NOT a requirement for a discrete probability distribution?

Accepted Answer

The outcomes must be measured on a continuous scale.

Question 3

Given the following probability distribution for the number of heads in two coin flips: $$P(0) = 0.25$$, $$P(1) = 0.5$$, $$P(2) = 0.25$$, what is the mean number of heads?

Accepted Answer

$$\mu = 1.00$$

Question 4

Which formula correctly calculates the variance $$\$$sigma^2$$ of a discrete probability distribution?

Accepted Answer

$$\$$sigma^2$$ = \sum_{i=1}^n (x_i - \mu)^2$ P(x_i)$$

Question 5

A call center in Atlanta has the following probability distribution for the number of rings before a call is answered: $$P(1) = 0.10$$, $$P(2) = 0.25$$, $$P(3) = 0.20$$, $$P(4) = 0.30$$, $$P(5) = 0.15. $$What is the expected number of rings before a call is answered?

Accepted Answer

$$\mu = 3.15$$

Question 6

Which of the following scenarios best fits a binomial experiment?

Accepted Answer

Testing 20 light bulbs to see how many are defective.

Question 7

If $$n = 10$$, $$p = 0.4$$, and $$q = 0.6$$, what is the probability of exactly 5 successes in a binomial distribution?

Accepted Answer

$$P(5,10) = 0.201$$

Question 8

What is the formula for the mean $$\mu of a $$binomial distribution?

Accepted Answer

$$\mu = np$$

Question 9

A bank receives an average of $$\lambda = 4$$ bad checks per week. What is the probability that it will receive exactly 3 bad checks next week (using the Poisson distribution)?

Accepted Answer

$$P(3) = 0.1954$$

Question 10

Which of the following is a requirement for using the Poisson distribution?

Accepted Answer

The number of occurrences in non-overlapping intervals must be independent.

Question 11

When can the Poisson distribution be used to approximate the binomial distribution?

Accepted Answer

When $$n \geq 20$$ and $$p \leq 0.05$$

Question 12

A quality control auditor randomly selects 10 accounts from a population of 50, where 5 are delinquent. What is the probability that at least one delinquent account is found (using the hypergeometric distribution)?

Accepted Answer

$$P(x \geq 1) = 0.69$$

Question 13

Which formula gives the probability of exactly $$x$$ successes in a hypergeometric distribution?

Accepted Answer

$$P(x) = \frac{\binom{R}{x} \binom{N-R}{n-x}}{\binom{N}{n}}$$

Question 14

Which of the following Excel functions would you use to calculate the probability of exactly $$x$$ successes in a binomial distribution?

Accepted Answer

=BINOM.DIST(x, n, p, FALSE)

Question 15

A Poisson distribution has a mean $$\lambda = 6. $$What is the variance of this distribution?

Accepted Answer

$$\$$sigma^2$$ = 6$$

Question 16

Which of the following best describes the expected monetary value (EMV)?

Accepted Answer

The mean of a discrete probability distribution when outcomes are in dollars.

Question 17

If a random variable $$X$$ has the following probability distribution: $$P(0) = 0.2$$, $$P(1) = 0.5$$, $$P(2) = 0.3$$, what is the variance $$\$$sigma^2$$ if $$\mu = 1.1$$?

Accepted Answer

$$\$$sigma^2$$ = 0.49$$

Question 18

Which of the following is NOT a property of a binomial experiment?

Accepted Answer

The probability of success changes from trial to trial.

Question 19

A Poisson process is being used to model the number of emails received per hour. Which of the following would violate the assumptions of the Poisson process?

Accepted Answer

The average rate of emails changes throughout the day.

Discrete Probability Distributions: Binomial, Poisson, and Hypergeometric

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