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Chapter 5: Q. 4 (page 309)

Liar, liar! Sometimes police use a lie detector test to help determine whether a suspect is

telling the truth. A lie detector test isn鈥檛 foolproof鈥攕ometimes it suggests that a person is

lying when he or she is actually telling the truth (a 鈥渇alse positive鈥�). Other times, the test

says that the suspect is being truthful when he or she is actually lying (a 鈥渇alse negative鈥�).

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.

Short Answer

Expert verified

a) The probability of the mammogram's false-negative rate must be interpreted.

b) We predict that around of people who take a8%(or0.08) polygraph.

Step by step solution

01

Part (a) Step 1: Given information

We have to tell what this probability means.

02

Part (a) Step 2: Explanation

  • The probability of the mammogram's false-negative rate must be interpreted.
  • The test says that the suspect is being truthful
03

Part (b) Step 1: Given information

We have to tell which is a more serious error in this case

04

Part (b) Step 2: Explanation

  • We predict that around 8%(or0.08)of people who take a polygraph.
  • The truth will have the polygraph show that they lie.

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Most popular questions from this chapter

Cell phones The Pew Research Center asked a random sample of 2024adult cell-phone owners from the United States their age and which type of cell phone they own: iPhone, Android, or other (including non-smartphones). The two-way table summarizes the data.

Suppose we select one of the survey respondents at random.

  1. Find P(iPhone | 18-34)
  2. Use your answer from part (a) to help determine if the events 鈥渋Phone鈥� and "18-34"are independent.

Butter side down Refer to the preceding exercise. Maria decides to test this

probability and drops 10 pieces of toast from a 2.5-foot table. Only 4of them land butter

side down. Maria wants to perform a simulation to estimate the probability that 4or

fewer pieces of toast out of 10would land butter side down if the researchers鈥� 0.81

probability value is correct.

a. Describe how you would use a table of random digits to perform the simulation.

b. Perform 3trials of the simulation using the random digits given. Copy the digits onto

your paper and mark directly on or above them so that someone can follow what you

did.

29077
14863
61683
47052
62224
51025
95052
90908
73592
75186
87136
95761
27102
56027
55892
33063
41842
81868

c. The dotplot displays the results of 50 simulated trials of dropping 10pieces of toast.

Is there convincing evidence that the researchers鈥� 0.81probability value is incorrect?

Explain your answer.

Dogs and cats In one large city, 40%of all households, own a dog, 32%

own a cat, and 18% own both. Suppose we randomly select a household and learn that the household owns a cat. Find the probability that the household owns a dog.

A basketball player claims to make 47%of her shots from the field. We want to simulate the player taking sets of 10shots, assuming that her claim is true.

To simulate the number of makes in 10shot attempts, you would perform the simulation as follows:

a. Use 10 random one-digit numbers, where 0-4are a make and 5-9are a miss.

b. Use 10random two-digit numbers, where 00-46are a make and 47-99are a miss.

c. Use 10random two-digit numbers, where 00-47are a make and 48-99are a miss.

d. Use 47random one-digit numbers, where 0is a make and 1-9are a miss.

e. Use 47random two-digit numbers, where 00-46are a make and 47-99are a miss.

Dogs and cats In one large city, 40%of all households own a dog, 32% own a cat, and 18% own both. Suppose we randomly select a household. What鈥檚 the probability that the household owns a dog or a cat?
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