Seeing the fishing pole in his grandfathers office, Ted Thorndikes first thought is that old Luke is

Question:

Seeing the fishing pole in his grandfather€™s office, Ted Thorndike€™s first thought is that old Luke is going to go fishing again and leave him to manage the store. He is quite surprised to learn the fishing pole is actually an inspiration for a new series of ads that Luke has in mind.
The elder Thorndike explains, €œTed, this fishing pole is made of graphite, the same stuff that goes into our Graf-Pro racquetball racquets. It€™s so flexible and strong that it can be bent so the two ends actually touch each other. They even show this in the ads.€ Although Luke realizes that you can€™t do exactly the same thing with a racquetball racquet, he€™d like to put some of his racquets into a horizontal mounting device, then see how much weight they€™ll take before they break.
If the amount of weight is impressive enough, Luke plans to include this kind of test in the television advertisements he€™s planning for the firm€™s racquetball racquets. However, he wants to be careful not to brag about the racquet being able to hold too much weight, since the firm could get into trouble with the government and other truth-in-advertising advocates.
He asks Ted to set up a test in which racquets are mounted horizontally, then the weight on the end is gradually increased until they break. Based on the test results, a weight value would be selected such that the average racquet would almost certainly be able to withstand this amount. Although accuracy is important, Ted has been instructed not to break more than 15 or 20 racquets in coming up with an average for all the racquets.
For 20 racquets subjected to this severe test, the weight (in pounds) at which each one failed was as follows. The data are also in file THORN09.

Ted believes it€™s reasonable to assume the population of breaking strengths is approximately normally distributed. Because of Luke€™s concern about being able to support the advertising claim, he wants to be very conservative in estimating the population mean for these breaking strengths. Ted needs some help in deciding how conservative he would like to be, and in coming up with a number that can be promoted in the ads.