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Chapter 5: Q .82. (page 341)

Media usage and good grades The Kaiser Family Foundation released a study about the influence of media in the lives of young people aged 8−18. 20 In the study, 17% of the youth were classified as light media users, 62% were classified as moderate media users, and 21% were classified as heavy media users. Of the light users who responded, 74% described their grades as good (A’s and B’s), while only 68% of the moderate users and 52% of the heavy users described their grades as good. Suppose that we select one young person from the study at random.

a. Draw a tree diagram to model this chance process.

b. Find the probability that this person describes his or her grades as good.

c. Suppose the chosen person describes his or her grades as good. What’s the probability that he or she is a heavy user of media?

Short Answer

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Part a)

Part b)

Part c)

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01

Part (a)Step 1:Given information

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Most popular questions from this chapter

2Drive to exercise : The two-way table summarizes the responses of 120 people to a survey in which they were asked, “Do you exercise for at least 30 minutes four or more times per week?” and “What kind of vehicle do you drive?”

ExerciseSedanSUVTruck
Yes251512
No202424

Suppose one person from this sample is randomly selected.

a. Find the probability that the person drives an SUV.

b. Find the probability that the person drives a sedan or exercises for at least 30 minutes four or more times per week.

c. Find the probability that the person does not drive a truck, given that she or he exercises for at least 30 minutes four or more times per week.

Checking independence Suppose C and D are two events such that

P(C)=0.6,P(D)=0.45,and P(C∩D)=0.3Are events C and D independent? Justify your answer.

Household size In government data, a household consists of all occupants of a dwelling unit. Choose an American household at random and count the number of people it contains. Here is the assignment of probabilities for the outcome. The probability of finding 3people in a household is the same as the probability of finding 4people.

a. What probability should replace “?” in the table? Why?

b. Find the probability that the chosen household contains more than 2people.

Checking independence Suppose A and B are two events such thatP(A)=0.3andP(B)=0.4, andP(A∩B)=0.12. Are events A and B independent? Justify your answer.

Will Luke pass the quiz ? Luke’s teacher has assigned each student in his class an online quiz, which is made up of 10multiple-choice questions with 4options each. Luke hasn’t been paying attention in class and has to guess on each question. However, his teacher allows each student to take the quiz three times and will record the highest of the three scores. A passing score is 6or more correct out of 10. We want to perform a simulation to estimate the score that Luke will earn on the quiz if he guesses at random on all the questions.

a. Describe how to use a random number generator to perform one trial of the simulation. The dotplot shows Luke’s simulated quiz score in 50trials of the simulation.

b. Explain what the dot at 1represents.

c. Use the results of the simulation to estimate the probability that Luke passes the quiz.

d. Doug is in the same class and claims to understand some of the material. If he scored 8points on the quiz, is there convincing evidence that he understands some of the material? Explain your answer.
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