Problem 63: Suppose a bill is considered late if it is paid after 20 days. In this case its "lateness" is the number of days over 20. For example, a bill paid 23 days after billing has a lateness of 3, whereas a bill paid 18 days after billing has a lateness of 0. Calculate a 95% confidence interval for the mean amount of lateness for all customers. Calculate similar confidence intervals for each customer size separately. Why is the distribution of lateness certainly not nor- mal? Do you think this matters for the validity of the confidence interval