1) Assume that an independent laboratory has tested 30-gallon trash bags as well as has found that none of the 30-gallon bags currently on the market has the mean breaking strength of 50 pounds or more. On the basis of these results, the producer of the new, improved trash bag feels sure that its 30-gallon bag will be the strongest such bag on the market if the new trash bag's mean breaking strength can be shown to be at least 50 pounds. The tested the breaking strengths of 40 trash bags of the new type that were selected during a 40-hour pilot production run.
The mean as well as the standard deviation of the sample of 40 trash bag breaking strengths are 50.575 for the sample mean and the standard deviation is 1.6438.
Employ the Empirical Rule and Z-score table to calculate estimates of tolerance intervals of all possible trash bag breaking strengths containing:
a) 68.26 percent,
b) 90.00 percent,
c) 95.44 percent,
d) 99.73 percent