The mean and the standard deviation of the sample of 40 trash bag breaking strengths in Table 1.9 are 50.575 and 1.6438, respectively.

a. Use the Excel output in Figure to calculate a t-based 95 percent confidence interval for μ, the mean of the breaking strengths of all possible new trash bags. Are we 95 percent confident that m is at least 50 pounds?

b. Assuming that the population of all individual trash bag breaking strengths is normally distributed, estimate tolerance intervals of the form [μ ± zα/2σ] that contain (1) 95 percent of all individual trash bag breaking strengths and (2) 99.8 percent of all individual trash bag breaking strengths.