Question: A worker randomly selects 16 packages from all the holiday packages received at a local parcel service. The sample has a mean weight of 27.5 pounds and a standard deviation of 3.2 pounds. Assume that the weights of holiday packages are known to be approximately normally distributed.

a) What is the point estimate for the true mean weight, , of all holiday packages received by the parcel service?

b) Calculate an interval estimate for the true mean weight, , of all packages received by the parcel service. In other words, construct a 95% confidence interval for the true mean weight, , of all packages received by the parcel service.

c) How many holiday packages must be randomly selected if we want 99% confidence that the sample mean weight is within 0.5 pounds of the population mean weight?