True or False? In Exercises 5–8, determine whether the statement is true or false. If it is false, rewrite it as a true statement.


For a random variable x, the word random indicates that the value of x is determined by chance.

Finding an Expected Value In Exercises 37 and 38, find the expected value E(x) to the player for one play of the game. If x is the gain to a player in a game of chance, then E(x) is usually negative. This value gives the average amount per game the player can expect to lose.

A high school basketball team is selling \(10 raffle tickets as part of a fund-raising program. The first prize is a trip to the Bahamas valued at \)5460, and the second prize is a weekend ski package valued at \$496. The remaining 18 prizes are \$100 gas cards. The number of tickets sold is 3500.

Baseball There were 116 World Series from 1903 to 2020. Use the probability distribution in Exercise 30 to find the number of World Series that had 4, 5, 6, 7, and 8 games. Find the population mean, variance, and standard deviation of the data using the traditional definitions. Compare to your answers in Exercise 30.

In Exercises 1–4, find the indicated probability using the geometric distribution.

Find P(5) when p = 0.09

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

Penalty Kicks Argentine soccer player Lionel Messi converts 78% of his penalty kicks. Suppose Messi takes six penalty kicks next season. Find the probability that the number he converts is (a) exactly six, (b) at most three, and (c) more than three. (Source: Transfermarkt)

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 attendance at concerts for a rock group

Constructing and Graphing Binomial Distributions In Exercises 27–30, (a) construct a binomial distribution, (b) graph the binomial distribution using a histogram and describe its shape, and (c) identify any values of the random variable x that you would consider unusual. Explain your reasoning.

College Acceptance Pennsylvania State University accepts 49% of applicants. You randomly select seven Pennsylvania State University applicants. The random variable represents the number who are accepted. (Source: US News & World Report)