Question

A car manufacturer recently reviewed the build time for 27 cars. The sample mean was 15 hours with a standard deviation of 6.94 hours. The build times are known to be normally distributed and the manufacturer wants to be 95% confident in the sample to represent the population. Determine the margin of error. One decimal place in final answer. Answer: What is the lower limit of the confidence interval? Answer: What is the upper limit of the confidence interval?

Answer 1

The margin of error is approximately 2.768 hours. The lower limit of the confidence interval is approximately 12.232 hours. The upper limit of the confidence interval is approximately 17.768 hours.

Step-by-step explanation:

To determine the margin of error and the lower and upper limits of the confidence interval, we can use the formula:

Margin of Error = Z * (Standard Deviation / sqrt(n))

Lower Limit = Sample Mean - Margin of Error

Upper Limit = Sample Mean + Margin of Error

Given the sample mean of 15 hours, standard deviation of 6.94 hours, and 95% confidence level, we need to find the z-value for the 95% confidence level. The z-value can be found using a standard normal distribution table, or using a calculator. For a 95% confidence level, the z-value is approximately 1.96.

Using the given values and the formula, we can calculate the margin of error:

Margin of Error = 1.96 * (6.94 / sqrt(27)) ≈ 2.768

The lower limit of the confidence interval is found by subtracting the margin of error from the sample mean:

Lower Limit = 15 - 2.768 ≈ 12.232 hours

The upper limit of the confidence interval is found by adding the margin of error to the sample mean:

Upper Limit = 15 + 2.768 ≈ 17.768 hours