Use the probability distribution in Exercise 3 to find the probability of randomly selecting a game in which DeMar DeRozan had (c) between two and four personal fouls, inclusive.

Linear Transformation of a Random Variable In Exercises 41 and 42, use this information about linear transformations. For a random variable x, a new random variable y can be created by applying a linear transformation , where a and b are constants. If the random variable x has mean and standard deviation , then the mean, variance, and standard deviation of y are given by the formulas

The mean annual salary of employees at an office is originally $46,000. Each employee receives an annual bonus of $600 and a 3% raise (based on salary). What is the new mean annual salary (including the bonus and raise)?

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.

Is the expected value of the probability distribution of a random variable always one of the possible values of x? Explain.v

Use the probability distribution in Exercise 3 to find the probability of randomly selecting a game in which DeMar DeRozan had (a) fewer than four personal fouls,

In Exercises 1–7, consider a grocery store that can process a total of four customers at its checkout counters each minute.

The mean number of arrivals per minute is four. Find the probability that

c. more than four customers will arrive during each of the first four minutes.

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.

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

Let x represent the length of time it takes to complete an exam.

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

Let x represent the populations of the 50 U.S. states.