Steeplechase horseraces are run on courses that include obstacles such as brush fences, stone walls, timber walls, and water jumps. A random sample of 17 winning times (in seconds) in the 23 8-mile...

Steeplechase horseraces are run on courses that include obstacles such as brush fences, stone walls, timber walls, and water jumps. A random sample of 17 winning times (in seconds) in the 23 8-mile Saratoga Steeplechase Race was obtained. The sample mean was
 Assume and
 he population distribution of winning times is normal, and find a one-sided 99% confidence interval, bounded below, for the true mean winning time.

There are actually infinitely many different confidence intervals for a population mean m. For example, suppose that, in a random sample of size n from a population with mean m, the underlying population is normal or n is large, and the population standard deviation s is known. One could start with a probability statement of the form