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. 

Find a 95% confidence interval for the mean amount of lateness for all customers. Find similar confidence intervals for each customer size separately. Why is the distribution of lateness certainly not normal? Do you think this matters for the validity of the confidence interval?