Each year in Liverpool, New York, a public librarian estimates the mean number of times the books in that library have been checked out in the previous year. To do this, the librarian randomly samples computer records for 100 books and forms a 95% confidence interval for the mean. This has been done for 20 years. Find the probability that

(a) all the confidence intervals contain the true means;

(b) at least one confidence interval does not contain the true mean.