Texting and Driving. In Exercises 21–26, refer to the accompanying table, which describes probabilities for groups of five drivers. The random variable x is the number of drivers in a group who say that they text while driving (based on data from an Arity survey of drivers).

Using Probabilities for Significant Events


a. Find the probability of getting exactly 3 drivers who say that they text while driving.

40% of consumers believe that cash will be obsolete in the next 20 years (based on a survey by J.P. Morgan Chase). In each of Exercises 15–20, assume that 8 consumers are randomly selected. Find the indicated probability.

Find the probability that at least 6 of the selected consumers believe that cash will be obsolete in the next 20 years.

Identifying Discrete and Continuous Random Variables. In Exercises 5 and 6, refer to the given values, then identify which of the following is most appropriate: discrete random variable, continuous random variable, or not a random variable.

a. IQ scores of statistics students

b. Exact heights of statistics students

c. Shoe sizes (such as 8 or 8½) of statistics students

d. Majors (such as history) of statistics students

e. The number of rolls of a die required for a statistics student to get the number 4

Exercises 33 and 34 involve the method of composite sampling, whereby a medical testing laboratory saves time and money by combining blood samples for tests so that only one test is conducted for several people. A combined sample tests positive if at least one person has the disease. If a combined sample tests positive, then individual blood tests are used to identify the individual with the disease or disorder.

HIV It is estimated that in the United States, the proportion of people infected with the human immunodeficiency virus (HIV) is 0.00343. In tests for HIV, blood samples from 50 different people are combined. What is the probability that the combined sample tests positive for HIV? Is it unlikely for such a combined sample to test positive?

Stem Cell Survey In a Newsweek poll of 882 adults, 481 (or 55%) said that they were in favor of using federal tax money to fund medical research using stem cells obtained from human embryos. A politician claims that people don’t really understand the stem cell issue and their responses to such questions are random responses equivalent to a coin toss. Use the following probabilities related to determining whether the result of 481 is significantly high (assuming the true rate is 50%). Is 481 significantly high? What should be concluded about the politician’s claim? Explain.

P(respondent says to use the federal tax money) = 0.5

P(among 882, exactly 481 says to use federal tax money) = 0.000713

P(among 882,481 or more say to use federal tax money) = 0.00389

In Exercises 5–12, determine whether the given procedure results in a binomial distribution or a distribution that can be treated as binomial (by applying the 5% guideline for cumbersome calculations). For those that are not binomial and cannot be treated as binomial, identify at least one requirement that is not satisfied.

Pew Survey In a Pew Research Center survey of 3930 subjects, the ages of the respondents are recorded.

In Exercises 5–12, determine whether the given procedure results in a binomial distribution or a distribution that can be treated as binomial (by applying the 5% guideline for cumbersome calculations). For those that are not binomial and cannot be treated as binomial, identify at least one requirement that is not satisfied.

In a Pew Research Center survey, 3930 subjects were asked if they have ever fired a gun, and the responses consist of “yes” or “no.”