Question 1

Which of the following best describes a discrete random variable?

Accepted Answer

A variable that takes on individually separate and distinct values, determined by chance.

Question 2

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

Accepted Answer

The probabilities must all be equal.

Question 3

Translate the statement: 'Buy at least twelve bottles of soda.' into an inequality for the random variable $$x.$$

Accepted Answer

$$x \geq 12$$

Question 4

Given the probability distribution: $$x = 1, 2, 3, 4, 5$$ with $$P(x) = 0.16, 0.22, 0.28, 0.20, 0.14$$, what is the probability that $$x is $$less than 5?

Accepted Answer

$$0.86$$

Question 5

Which of the following tables does NOT represent a probability distribution?

Accepted Answer

A table where one probability is negative.

Question 6

If $$P(x) is $$the probability that $$x$$ people out of five have a certain gene, and $$P(2) = 0.1699$$ and $$P(4) = 0.2791$$, what is the probability that either two or four people have the gene?

Accepted Answer

$$0.4490$$

Question 7

Which formula correctly calculates the mean $$\mu of a $$discrete probability distribution?

Accepted Answer

$$\mu = \sum [x \cdot P(x)]$$

Question 8

A probability distribution has $$\mu = 2.5$$ and $$\sigma = 1.2. $$Using the rule of thumb for unusual values (more than two standard deviations from the mean), which value of $$x$$ would be considered unusual?

Accepted Answer

$$x = 5$$

Question 9

Which scenario best fits the requirements for a binomial distribution?

Accepted Answer

Counting the number of heads in 10 coin flips.

Question 10

A survey finds that 41% of women prefer reading as a leisure activity. If you randomly select 4 women, what is the probability that at least 2 of them prefer reading? (Let $$X be $$the number who prefer reading.)

Accepted Answer

$$P(X \geq 2) = 1 - P(X = 0) - P(X = 1)$$

Question 11

Given a binomial distribution with $$n = 8$$ and $$p = 0.10$$, what is the mean number of successes?

Accepted Answer

$$\mu = n \cdot p = 0.8$$

Question 12

If a probability distribution has $$\mu = 1.5$$ and $$\sigma = 0.5$$, what is the variance?

Accepted Answer

$$\$$sigma^2$$ = 0.25$$

Question 13

A company survey uses the following probability distribution for ratings: $$x = 1, 2, 3, 4, 5$$ with $$P(x) = 0.16, 0.22, 0.28, 0.20, 0.14. $$What is the expected value (mean) of the ratings?

Accepted Answer

$$\mu = 2.94$$

Question 14

Which of the following is a valid probability statement for a discrete random variable $$X$$?

Accepted Answer

$$P(X = 1) = 0.3$$

Question 15

A probability distribution for the number of tails in three coin flips is given as $$P(0) = 0.125$$, $$P(1) = 0.375$$, $$P(2) = 0.375$$, $$P(3) = 0.125. $$What is the variance $$\$$sigma^2$$?

Accepted Answer

$$\$$sigma^2$$ = 0.75$$

Question 16

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

Accepted Answer

The probability of success changes from trial to trial.

Question 17

If $$P(x) is $$the probability that $$x$$ people out of five have a gene, what is the probability that fewer than two people have the gene?

Accepted Answer

$$P(0) + P(1)$$

Question 18

A probability distribution has $$\mu = 2.0$$ and $$\sigma = 0.8. $$Using the rule of thumb, which value would be considered unusual?

Accepted Answer

$$x = 4.0$$

Question 19

Which of the following best describes the expected value in a probability distribution?

Accepted Answer

The average value you would expect after many trials.

Discrete Probability Distributions: Study Notes for Introductory Statistics (Chapter 5)

Study Guide - Practice Questions

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