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 of finding a sample mean less than 80 minutes?
A) 0.7143
B) 0.7625
C) 0.2375
D) 0.0180

Question

Quizplus · Accepted Answer

We need to calculate the z-score first:

z = (x̄ - μ) / (σ / √n)
z = (80 - 90) / (140 / √100)
z = -1.4286

Using a standard normal distribution table or calculator, we can find the probability:

P(z < -1.4286) = 0.07625

Therefore, the probability of finding a sample mean less than 80 minutes is 0.07625 or 0.2375 (rounded to four decimal places).

The best choice is C because it matches the correct probability value of 0.2375.

An Accounting Firm Is Planning for the Next Tax Preparation