A butcher shop manager wants to know how much on average customers spend per visit. Previous research suggests that the population standard deviation is $11.05. The manager found a mean value of $65.50 for a random sample of 40 customers, and wants to construct a 95% confidence interval for the mean value.

a) What is the critical z-value that will need to be used to calculate the confidence interval?

(b) What is the 95% confidence interval?

(c) If the manager wants a margin of error within $1, how large of a sample size will they need?