An accounting firm is planning for the next tax preparation season. From last year's returns, the firm collects a systematic random sample of 100 filings. The 100 filings showed an average preparation time of 90 minutes with a standard deviation of 140 minutes. What is the probability that the mean completion time is between 1 and 2 hours, i.e., 60 and 120 minutes?
A) Approximately 1.
B) 0.1664
C) 0.8336
D) 0.9676
E) None of the choices are correct

Question

Quizplus · Accepted Answer

The probability that the mean completion time is between 1 and 2 hours is 0.9676. This is because the standard deviation is 140 minutes, and the mean is 90 minutes. The z-score for a completion time of 60 minutes is (60 - 90) / 140 = -0.2143. The z-score for a completion time of 120 minutes is (120 - 90) / 140 = 0.2143. The probability that the mean completion time is between 1 and 2 hours is the area under the normal curve between -0.2143 and 0.2143, which is 0.9676.

An Accounting Firm Is Planning for the Next Tax Preparation