UberEATS wants to estimate the mean dollar value per customer order. The company takes a random sample of 80 orders and finds a mean of $35.50 with a standard deviation of $2.75. Assume the conditions are satisfied and do NOT need to be checked.

a) Calculate the 99% confidence interval.

b) Interpret the confidence interval.

c) Explain how, if at all, the width of your confidence interval changes if the sample size was decreased to 40 orders, holding all else the same.