A growing niche in the restaurant business is gourmet-casual breakfast, lunch, and brunch. Chains in this group include Panera Bread. Suppose that the mean per-person check for breakfast at Panera Bread is approximately $9.50.

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

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