Suppose Rebco can earn interest at the rate of 0.011% daily on excess cash. The company realizes that it could earn extra interest if its customers paid their bills more promptly.
a. Find a 95% confidence interval for the mean amount of interest it could gain if each of its customers paid exactly one day more promptly. Find similar confidence intervals for each customer class separately.
b. Suppose these 91 billings represent a random sample of the 2792 billings Rebco generates during the year. Find a 95% confidence interval for the total amount of extra interest it could gain by getting each of these 2792 billings to be paid two days more promptly.