Finding and Interpreting Mean, Variance, and Standard Deviation In Exercises 31–36, find the mean, variance, and standard deviation of the binomial distribution for the given random variable. Interpret the results and determine any unusual values.


Life on Other Planets Seventy-nine percent of U.S. adults believe that life on other planets is plausible. You randomly select eight U.S. adults and ask them whether they believe that life on other planets is plausible. The random variable represents the number who believe that life on other planets is plausible. (Source: Ipsos)

Finding and Interpreting Mean, Variance, and Standard Deviation In Exercises 31–36, find the mean, variance, and standard deviation of the binomial distribution for the given random variable. Interpret the results and determine any unusual values.

Late for Work Thirty-one percent of U.S. employees who are late for work blame oversleeping. You randomly select 12 U.S. employees who are late for work and ask them whether they blame oversleeping. The random variable represents the number who are late for work and blame oversleeping. (Source: CareerBuilder)

Multinomial Experiments In Exercises 39 and 40, use the information below.

A multinomial experiment satisfies these conditions.

The experiment has a fixed number of trials n, where each trial is independent of the other trials.

Each trial has k possible mutually exclusive outcomes:

Each outcome has a fixed probability. So, . The sum of the probabilities for all outcomes is

The number of times occurs is , the number of times occurs is , the number of times occurs is , and so on.

The discrete random variable x counts the number of times that each outcome occurs in n independent trials where . The probability that x will occur is

Genetics According to a theory in genetics, when tall and colorful plants are crossed with short and colorless plants, four types of plants will result: tall and colorful, tall and colorless, short and colorful, and short and colorless, with corresponding probabilities of , and . Ten plants are selected. Find the probability that 5 will be tall and colorful, 2 will be tall and colorless, 2 will be short and colorful, and 1 will be short and colorless.

"Multinomial Experiments In Exercises 39 and 40, use the information below.

A multinomial experiment satisfies these conditions.

The experiment has a fixed number of trials n, where each trial is independent of the other trials.

Each trial has k possible mutually exclusive outcomes:

Each outcome has a fixed probability. So, . The sum of the probabilities for all outcomes is

The number of times occurs is , the number of times occurs is , the number of times occurs is , and so on.

The discrete random variable x counts the number of times that each outcome occurs in n independent trials where . The probability that x will occur is

Genetics Another proposed theory in genetics gives the corresponding probabilities for the four types of plants described in Exercise 39 as , and . Ten plants are selected. Find the probability that 5 will be tall and colorful, 2 will be tall and colorless, 2 will be short and colorful, and 1 will be short and colorless."

Discrete Variables and Continuous Variables In Exercises 13–18, determine whether the random variable x is discrete or continuous. Explain.

Let x represent the fitted hat sizes of members of a softball team.

Graphical Analysis In Exercises 9–12, determine whether the graph on the number line represents a discrete random variable or a continuous random variable. Explain your reasoning.

The distance a baseball travels after being hit

Finding Binomial Probabilities In Exercises 19–26, find the indicated probabilities. If convenient, use technology or Table 2 in Appendix B.

Civil Rights Fifty-nine percent of U.S. adults think that civil rights for Black Americans have improved during their lifetime. You randomly select seven U.S. adults. Find the probability that the number who think that civil rights for Black Americans have improved during their lifetime is (a) exactly one and (b) exactly five. (Source: Gallup)