The manager of a cleaning supply store wants to estimate the actual amount of bleach contained in 1-gallon bottles purchased from a nationally known brand manufacturer. The manufacturer's specifications state that the standard deviation of the amount of bleach is equal to 0.02 gallon. A random sample of 64 bottles is selected. The sample mean amount of bleach per 1-gallon bottle is 0.992 gallon.

a.Construct a 99% confidence interval estimate of the population mean amount of bleach included in a 1-gallon bottle.

b.On the basis of your 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 bleach per bottle is normally distributed here? Explain.

d.Construct a 95% confidence interval estimate. How does this change your answer to (b)?