The company Tasty Market wants to find new packaging for its pralines. The management is still unsure about which colour to use. Previously, the pralines were packaged in yellow. Now a blue colour is in discussion.

(a) As part of a market research study in 25 of the 200 Tasty Market stores, you must investigate the effect of packaging colour on weekly sales. Assume that sales follow a normal distribution. For the blue packaging, you identify average weekly sales of 9982 packages and an empirical standard deviation of 410 packages. Calculate the 90% confidence interval for the expected sales.

(b) How does the confidence interval change if you select a higher confidence level? Explain your answer.

(c) What is the true empirical standard deviation with a probability of at least 99.5%?