A set of telephone lines is to be installed so as to connect town A to town B. The town A has 2000 telephones. If each of the telephone users of A were to be guaranteed instant access to make calls to B, 2000 telephone lines would be needed. This would be rather extravagant. Suppose that during the busiest hour of the day each subscriber in A requires, on the average, a telephone connection to B for two minutes, and that these telephone calls are made at random. Find the minimum M of telephone lines to B which must be installed so that at most only 1 percent of the callers to town A will fail to have immediate access to a telephone line to B.
Book mentions approximating the distribution by a Gaussian distribution to facilitate the arithmetic.
The Attempt at a Solution
What does the author mean by "the random telephone calls"? Does that mean that every 2 minutes a random number of subscriber lines is turned on (assuming 0 to 2000)? By the way if calls are evenly distributed in the hour every two minutes- I think we would need 2000/30 lines. If calls are made at random, it wouldn't be evenly distributed in the hour. Help is appreciated.