Bones Brothers & Associates prepare individual tax returns. Over prior years, Bones Brothers has maintained careful records regarding the time to prepare a return. The mean time to prepare a return is 90 minutes and the standard deviation of this distribution is 14 minutes. Suppose 100 returns from this year are selected and analyzed regarding the preparation time. What is the probability that the mean time for the sample of 100 returns is between 88 minutes and 92 minutes?
A) Approximately 1
B) 0.1664
C) 0.8336
D) 0.8472

Question

Quizplus · Accepted Answer

The probability that the mean time for the sample of 100 returns is between 88 minutes and 92 minutes is 0.8472. This is because the sample mean is normally distributed with a mean of 90 minutes and a standard deviation of 14 minutes / sqrt(100) = 1.4 minutes. Therefore, the z-score for a sample mean of 88 minutes is (88 - 90) / 1.4 = -1.43, and the z-score for a sample mean of 92 minutes is (92 - 90) / 1.4 = 1.43. The probability that the sample mean is between 88 minutes and 92 minutes is the area under the normal curve between these two z-scores, which is 0.8472.

Bones Brothers & Associates Prepare Individual Tax Returns