A traffic engineer plans to estimate the average number of cars that pass through an intersection each day. Based on previous studies the standard deviation is believed to be 52 cars. She wants to estimate the mean to within ±10 cars with 90 percent confidence. The needed sample size for n is:
A) n = 104 days.
B) n = 74 days.
C) n = 10 days.
D) n = 9 days.

Question

Quizplus · Accepted Answer

To calculate the sample size needed to estimate the mean with a certain level of confidence and margin of error, the formula is $n = \left(\frac{Z \cdot \sigma}{E}\right)^2$, where $Z$ is the Z-score corresponding to the confidence level, $\sigma$ is the standard deviation, and $E$ is the margin of error. For a 90% confidence level, the Z-score is approximately 1.645. Given $\sigma = 52$ cars and $E = 10$ cars, substituting these values into the formula gives $n = \left(\frac{1.645 \cdot 52}{10}\right)^2 \approx 73.68$, which rounds up to 74 days.

A Traffic Engineer Plans to Estimate the Average Number of Cars