If tire kingdom installs automobile tires on a first-come first-served basis. a random sample of 50 customers experienced an average wait time of 93.7 minutes. The 99% confidence interval for the sample average wait time is 85.89 minutes, 101.51 minutes.
What is the confidence interval?
To determine the 99% confidence interval for the sample average wait time use the formula:
Confidence interval = Sample mean ± (Critical value * Standard deviation / √n)
For a 99% confidence level and 50 degrees of freedom (n - 1) the critical value is 2.680.
Substitute the values into the formula:
Confidence interval = 93.7 minutes ± (2.680 * 20.6 minutes / √50)
Confidence interval = 93.7 minutes ± (2.680 * 20.6 minutes / 7.071)
Confidence interval = 93.7 minutes ± 7.81 minutes
Therefore the 99% confidence interval for the sample average wait time is 85.89 minutes, 101.51 minutes.
Based on the provided sample, this indicates that we have 99% confidence that the true population average wait time is within this range.