Question 1

Which of the following statements best describes a discrete random variable?

Accepted Answer

A variable that takes on individually separate and distinct values, such as the number of people in a room.

Question 2

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

Accepted Answer

$$x \geq 12$$

Question 3

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

Accepted Answer

The random variable must be continuous.

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 valid probability distribution?

Accepted Answer

A table where one probability is negative.

Question 6

If a probability distribution has $$x$$ values of 0, 1, 2, 3, 4, 5 and corresponding probabilities $$0.1302, 0.3104, 0.1699, 0.0997, 0.2791, 0.0107$$, what is the probability that at least one person out of five has the gene?

Accepted Answer

$$0.8698$$

Question 7

Given the same distribution as above, what is the probability that fewer than two people out of five have the gene?

Accepted Answer

$$0.4406$$

Question 8

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

Accepted Answer

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

Question 9

For 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 mean $$\mu$$?

Accepted Answer

$$\mu = 2.94$$

Question 10

A probability distribution has $$x$$ values of 0, 1, 2, 3, 4, 5$$ and P(x) = 0.1302$$, 0.3104, 0.1699, 0.0997, 0.2791, 0.0107$. What is the probability that exactly three people out of five have the gene?

Accepted Answer

$$0.0997$$

Question 11

Which of the following is the correct formula for the variance $$\$$sigma^2$$ of a discrete probability distribution?

Accepted Answer

$$\$$sigma^2$$ = \sum [x^2$ \cdot P(x)] - \mu^2$

Question 12

A probability distribution has a mean $$\mu = 1.5$$ and standard deviation $$\sigma = 0.5. $$According to the empirical rule, which value would be considered unusual?

Accepted Answer

$$2.7$$

Question 13

Given a binomial experiment with $$n = 5$$ and $$p = 0.3$$, what is the probability of exactly 2 successes? (Use the binomial formula: $$P(x) = \binom{n}{x} p^x (1-p$$)^{n-x}$$)

Accepted Answer

$$0.3087$$

Question 14

Which of the following scenarios is NOT a binomial experiment?

Accepted Answer

Counting the number of red marbles drawn from a jar without replacement.

Question 15

A survey finds that 41% of women consider reading their favorite leisure activity. If you randomly select 4 women, what is the probability that at least 2 say yes? (Use binomial probability.)

Accepted Answer

$$0.563$$

Question 16

If a probability distribution has $$\mu = 2.5$$ and $$\sigma = 0.7$$, what is the range of usual values (within two standard deviations of the mean)?

Accepted Answer

$$1.1 to$$ $$3.9$$

Discrete Probability Distributions: Introductory Statistics Ch. 5 Study Notes

Study Guide - Practice Questions

Study Guide - Flashcards