Chapter 5: Q. 47 (page 328)
Dogs and cats In one large city, of all households own a dog, own a cat, and own both. Suppose we randomly select a household. What’s the probability that the household owns a dog or a cat?
The likelihood that the household owns either a dog or a cat is
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Smartphone addiction? A media report claims that of U.S. teens with smartphones feel addicted to their devices. A skeptical researcher believes that this figure is too high. She decides to test the claim by taking a random sample of U.S. teens who have smartphones. Only of the teens in the sample feel addicted to their devices. Does this result give convincing evidence that the media report’s claim is too high? To find out, we want to perform a simulation to estimate the probability of getting or fewer teens who feel addicted to their devices in a random sample of size from a very large population of teens with smartphones in which 50% feel addicted to their devices.
Let = feels addicted and = doesn’t feel addicted. Use a random number generator to produce random integers from to . Record the number of ’s in the simulated random sample. Repeat this process many, many times. Find the percent of trials on which the number of ’s was or less.
Liar, liar! Sometimes police use a lie detector test to help determine whether a suspect is
telling the truth. A lie detector test isn’t foolproof—sometimes it suggests that a person is
lying when he or she is actually telling the truth (a “false positive”). Other times, the test
says that the suspect is being truthful when he or she is actually lying (a “false negative”).
For one brand of lie detector, the probability of a false positive is 0.08.
a. Explain what this probability means.
b. Which is a more serious error in this case: a false positive or a false negative? 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 multiple-choice questions with options 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 or more correct out of . 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 trials of the simulation.
b. Explain what the dot at represents.
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 points on the quiz, is there convincing evidence that he understands some of the material? Explain your answer.
Income tax returns Here is the distribution of the adjusted gross income (in thousands of dollars) reported on individual federal income tax returns in a recent year:
a. What is the probability that a randomly chosen return shows an adjusted gross income of or more?
b. Given that a return shows an income of at least , what is the conditional
probability that the income is at least ?
Body image A random sample of U.S. college students was asked, “What is your perception of your own body? Do you feel that you are overweight, underweight, or about right?” The two-way table below summarizes the data on perceived body image by gender.
Suppose we randomly select one of the survey respondents.
a. Given that the person perceived his or her body image as about right, what’s the
probability that the person is female?
b. If the person selected is female, what’s the probability that she did not perceive her body image as overweight?
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