The manager of the service department of a local car dealers

The manager of the service department of a local car dealership has noted that the service times of a sample of 30 new automobiles has a standard deviation of 6 minutes. A 95% confidence interval estimate for the standard deviation of the service times for all their new automobiles is

Solution

We know that the standard deviation of a sampling distribution is its standard error. A 95 % confidence interval ,in case of a normal distribution, is determined by adding and subtracting 1.96 times standard deviations to/from the mean. Here, the mean has not been given. Let us assume the mean of the service times of a sample of 30 new automobiles to be x minutes. Since 1.96*6 minutes = 11.76 minutes, hence, the 95 % confidence interval is [ x-11.76,x+11.76].