Question

researcher wants to find the mean diameter of the washers produced in a company and takes 120 washers as a sample size. The result is that the average diameter of the washers produced by the company is 28 inches. If the standard deviation of the manufacturing process is 0.5, and the confidence level is 99%, what is the margin of error of the mean? Round your answer to three decimal places.(1 point)

Answer 1

To calculate the margin of error of the mean, we can use the formula:

Margin of error = Z * (Standard deviation / sqrt(sample size))

First, we need to find the Z-value for a 99% confidence level. This can be found using a Z-table or a calculator. For a 99% confidence level, the Z-value is approximately 2.576.

Now plug in the values into the formula:

Margin of error = 2.576 * (0.5 / sqrt(120))
Margin of error = 2.576 * (0.5 / 10.954)
Margin of error = 2.576 * 0.0457
Margin of error ≈ 0.117

Therefore, the margin of error of the mean is approximately 0.117 inches.