Lesson 5.4 Checkpoint

A federal report finds that lie detector tests given to truthful persons have probability 0.2 of suggesting that the person is deceptive. A company asks 12 job applicants about thefts from previous employers, using a lie detector to assess their truthfulness. Suppose that all 12 answer truthfully. Let X = the number of people whom the lie detector identifies as being deceptive.

Calculate and interpret the mean of X.

(LT 5.4.1 #1)

• μ_X = 12

  If many, many different groups of 12 job applicants are given a lie detector test, we expect about 12 of them will be identified as deceptive, on average.

• μ_X = 0.2

  If many, many different groups of 12 job applicants are given a lie detector test, we expect about 0.2 of them will be identified as deceptive, on average.

• μ_X = 2.4

  If many, many different groups of 12 job applicants are given a lie detector test, we expect about 2.4 of them will be identified as deceptive, on average.

• μ_X = 12

  If many, many different groups of 2.4 job applicants are given a lie detector test, we expect about 0.2 of them will be identified as deceptive, on average.

A federal report finds that lie detector tests given to truthful persons have probability 0.2 of suggesting that the person is deceptive. A company asks 12 job applicants about thefts from previous employers, using a lie detector to assess their truthfulness. Suppose that all 12 answer truthfully. Let X = the number of people whom the lie detector identifies as being deceptive.

Calculate and interpret the standard deviation of X.

(LT 5.4.1 #2)

• σ_X = 1.549

  The number of applicants labeled as deceptive by the lie detector test would typically vary by about 1.549 from the mean of 2.4.

• σ_X = 1.386

  The number of applicants labeled as deceptive by the lie detector test would typically vary by about 1.386 from the mean of 2.4.

• σ_X = 3.464

  The number of applicants labeled as deceptive by the lie detector test would typically vary by about 3.464 from the mean of 2.4.

• σ_X = 1.92

  The number of applicants labeled as deceptive by the lie detector test would typically vary by about 1.92 from the mean of 2.4.

When rolling two fair, 6-sided dice, the probability of rolling doubles is 1/6. Suppose Elias rolls the dice 4 times. Let W = the number of times he rolls doubles. The probability distribution of W is shown here.

Find the probability that Elias rolls doubles more than twice.

(LT 5.4.2 #1)

• 0.116

• 0.868

• 0.132

• 0.016

About 20% of cars sold in North America are white. Let’s assume that the color of any car on the road is independent of cars that come before or after it and that the proportion of white cars is the same throughout North America. The probability distribution of X = the number of white cars among 6 randomly selected cars is given here.

You are standing on a bridge over an interstate highway, and 4 of the next 6 cars that pass by are white.

Does this suggest that the proportion of white cars that use this particular highway is greater than 0.20?

Find the probability that at least 4 cars in randomly selected groups of 6 cars are white and use this to justify your answer. Select all correct responses.

(LT 5.4.2 #2)

• 0.0170

• 0.0016

• Because this outcome is unlikely, we have convincing evidence that the proportion of white cars that use this particular highway is greater than 0.20

• Because this outcome is likely, we don't have convincing evidence that the proportion of white cars that use this particular highway is greater than 0.20

The makers of a diet cola claim that its taste is indistinguishable from the taste of the full-calorie version of the same cola. To investigate, a statistics student named Emily prepared small samples of each type of soda in identical cups. Then she had volunteers taste each cola in random order and try to identify which was the diet cola and which was the regular cola. If we assume that the volunteers couldn’t tell the difference, each one was guessing, with a 1/2 chance of being correct. Let X = the number of volunteers who correctly identify the colas.

Of the 30 volunteers, 23 made correct identifications. Does this give convincing evidence that the volunteers can taste the difference between the diet and regular colas?

(LT 5.4.3 #1)

Compute P(X ≥ 23) with technology and use this result to support your answer.

Select ALL Correct answers!

• 0.0026

• 0.9993

• Because this outcome is very unlikely, we have convincing evidence that at least some volunteers can taste the difference between diet and regular sodas.

• Because this outcome is very likely, we don't have convincing evidence that at least some volunteers can taste the difference between diet and regular sodas.