A growing niche in the restaurant business is gourmet- casual breakfast, lunch, and brunch. Chains in this group include Egg Spectation and Panera Bread. Suppose that the mean per- person check for breakfast at EggSpectation is approximately $ 14.50.

a. Assuming a standard deviation of $ 2.00, what sample size is needed to estimate, with 95% confidence, the mean per- person check for EggSpectation to within ± $0.25?

b. Assuming a standard deviation of $ 2.50, what sample size is needed to estimate, with 95% confidence, the mean per- person check for EggSpectation to within ± $0.25?

c. Assuming a standard deviation of $ 3.00, what sample size is needed to estimate, with 95% confidence, the mean per- person check for EggSpectation to within ± $0.25?

d. Discuss the effect of variation on the sample size needed.