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

95% confidence interval estimate for the standard deviation = [4.78 , 8.06]

Step-by-step explanation:

We are given that 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, i.e. n = 30 and s = 6.

The pivotal quantity for 95% confidence interval for the population variance is given by;

                     ~

95% confidence interval for the population variance is;

P(16.05 < < 45.72) = 0.95

P(16.05 < < 45.72) = 0.95

P( < < ) = 0.95

P( < <  ) = 0.95

95% Confidence interval for = [ , ]

                                                = [ , ]

                                                = [ 22.835 , 65.047 ]

So, 95% Confidence interval for = [ ] = [ 4.78 , 8.06 ]

Therefore, 95% confidence interval for the standard deviation of the service times for all their new automobiles is [ 4.78 , 8.06 ] .