The manager of a paint supply store wants to estimate the actual amount of paint contained in 1-gallon cans purchased from a nationally known manufacturer. The manufacturer's specifications state that the standard deviation of the amount of paint is equal to 0.02 gallon. A random sample of 50 cans is selected, and the sample mean amount of paint per 1-gallon can is 0.995 gallon.
a. Construct a 99% confidence interval estimate for the population mean amount of paint included in a 1-gallon can.
b. On the basis of these results, do you think that the manager has a right to complain to the manufacturer? Why?
c. Must you assume that the population amount of paint per can is normally distributed here? Explain.
d. Construct a 95% confidence interval estimate. How does this change your answer to (b)?