chapter 6

The commuting time for a student to travel from home to a college campus is normally distributed with a mean of 30 minutes and a standard deviation of 5 minutes. If the student leaves home at 8:25 A.M., what is the probability that the student will arrive at the college campus later than 9 A.M.?

• 0.16

• 0.32

• 0.50

• 0.84

• 1.00

A mathematics competition uses the following scoring procedure to discourage students from guessing (choosing an answer randomly) on the multiple-choice questions. For each correct response, the score is 7. For each question left unanswered, the score is 2. For each incorrect response, the score is 0. If there are 5 choices for each question, what is the minimum number of choices that the student must eliminate before it is advantageous to guess among the rest?

• 0

• 1

• 2

• 3

• 4

Two friends, Andy and Bob, participate in a game of bowling every week. From past experiences, it is known that both friends’ scores are approximately normally distributed, where Andy has a mean score of 150 with a standard deviation of 30, and Bob has a mean score of 165 with a standard deviation of 15. Assuming that their scores are independent, which of the following values is closest to the probability that Andy will have a greater score than Bob in a single game?

• 0.16

• 0.28

• 0.31

• 0.33

• 0.37

The distribution of heights of 6-year-old girls is approximately normally distributed with a mean of 46.0 inches and a standard deviation of 2.7 inches. Aliyaah is 6 years old, and her height is 0.96 standard deviation above the mean. Her friend Jayne is also 6 years old and is at the 93rd percentile of the height distribution. At what percentile is Aliyaah’s height, and how does her height compare to Jayne’s height?

• (A) Aliyaah’s height is at the 17th percentile of the distribution, and she is shorter than Jayne.

• (B) Aliyaah’s height is at the 67th percentile of the distribution, and she is shorter than Jayne.

• (C) Aliyaah’s height is at the 67th percentile of the distribution, and she is taller than Jayne.

• (D) Aliyaah’s height is at the 83rd percentile of the distribution, and she is shorter than Jayne.

• (E) Aliyaah’s height is at the 83rd percentile of the distribution, and she is taller than Jayne.

A random variable X has a mean of 120 and a standard deviation of 15. A random variable Y has a mean of 100 and a standard deviation of 9. If X and Y are independent, approximately what is the standard deviation of X - Y?

• 24.0

• 17.5

• 12.0

• 6.0

• 4.9