In problem 6–21, give a 99% confidence interval for the variance of the number of miles that may be driven on a tire.

problem 6–21

A tire manufacturer wants to estimate the average number of miles that may be driven on a tire of a certain type before the tire wears out. A random sample of 32 tires is chosen; the tires are driven on until they wear out, and the number of miles driven on each tire is recorded. The data, in thousands of miles, are as follows:

32, 33, 28, 37, 29, 30, 25, 27, 39, 40, 26, 26, 27, 30, 25, 30, 31, 29, 24, 36, 25, 37, 37, 20, 22, 35, 23, 28, 30, 36, 40, 41

Give a 99% confidence interval for the average number of miles that may be driven on a tire of this kind.