In order to fairly set flat rates for auto mechanics, a shop foreman needs to estimate the average time it takes to replace a fuel pump in a car. How large a sample must he select if he wants to be 99% confident that the true
Average time is within 15 minutes of the sample average? Assume the standard deviation of all times is 30
Minutes.
A)27
B)26
C)6
D)5

Question

Quizplus · Accepted Answer

To determine the sample size needed for a specific confidence level and margin of error, the formula is $n = \left(\frac{Z \cdot \sigma}{E}\right)^2$, where $n$ is the sample size, $Z$ is the Z-score corresponding to the desired confidence level, $\sigma$ is the population standard deviation, and $E$ is the margin of error. For a 99% confidence level, the Z-score is approximately 2.576. Given $\sigma = 30$ minutes and $E = 15$ minutes, substituting these values into the formula gives $n = \left(\frac{2.576 \cdot 30}{15}\right)^2 = \left(\frac{77.28}{15}\right)^2 \approx 26.45$, which rounds up to 27 to ensure the sample is large enough.

In Order to Fairly Set Flat Rates for Auto Mechanics