5. Binomial Distribution & Discrete Random Variables

The table lists the number of wireless devices per household in a small town in the United States.

c. Find the mean, variance, and standard deviation of the probability distribution and interpret the results.

In Exercises 5–8, assume that the Poisson distribution applies; assume that the mean number of Atlantic hurricanes in the United States is 5.5 per year, as in Example 1; and proceed to find the indicated probability.

b. In a 118-year period, how many years are expected to have 10 hurricanes?

The table lists the number of wireless devices per household in a small town in the United States.

a. Construct a probability distribution.

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

"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.

The mean of the random variable of a probability distribution describes how the outcomes vary."

In Exercises 1 and 2, determine whether the random variable x is discrete or continuous. Explain.

Let x represent the grade on an exam worth a total of 100 points.

A student is analyzing different types of variables in a statistics class. Which of the following below is a discrete random variable?

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.

The table shows the ages of students in a freshman orientation course.

b. Graph the probability distribution using a histogram and describe its shape.

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.

The Centers for Disease Control and Prevention (CDC) is required by law to publish a report on assisted reproductive technology (ART). ART includes all fertility treatments in which both the egg and the sperm are used. These procedures generally involve removing eggs from a patient’s ovaries, combining them with sperm in the laboratory, and returning them to the patient’s body or giving them to another patient.

You are helping to prepare a CDC report on young ART patients and select at random 6 ART cycles of patients under 35 years of age for a special review. None of the cycles resulted in a live birth. Your manager feels it is impossible to select at random 10 ART cycles that do not result in a live birth. Use the pie chart at the right and your knowledge of statistics to determine whether your manager is correct.

b. What probability distribution do you think best describes the situation? Do you think the distribution of the number of live births is discrete or continuous? Explain your reasoning.

Finding the Mean, Variance, and Standard Deviation In Exercises 29–34, (a) find the mean, variance, and standard deviation of the probability distribution, and (b) interpret the results.

Machine Parts The number of defects per 1000 machine parts inspected

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.

Discrete or Continuous? Is the random variable given in the table from Exercise 1 discrete or continuous? Explain.

In Exercises 3 and 4, (a) construct a probability distribution, and (b) graph the probability distribution using a histogram and describe its shape.

The number of hours students in a college class slept the previous night