A call centre knows that each call to its helpline is answered at the first ring with probability…

A call centre knows that each call to its helpline is answered at the first ring with probability $0.4$, independently of the other calls. On a busy afternoon, the centre receives $200$ calls. The manager wants to know how likely it is that at most $70$ of them are answered at the first ring, because that would trigger a review of staffing. Counting all the terms of the binomial distribution by hand is slow, so she uses the normal approximation with a continuity correction. Find the mean and the standard deviation of the number of calls answered at the first ring. Then find the approximate probability that at most $70$ are answered at the first ring. Give the answers to four decimal places, and use a calculator or the program for the standard normal distribution function.