math (unanswered, previously posted)
posted by Edward .
A set of telephone lines is to be installed so as to connect between town A and 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 supscriber 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 number M of telephone lines to B which must be installed so that at most, only 1% of the callers of town A will fail to have immediate access to a telephone line to B. (Suggestion!: approximate the distribution by a Gaussian distribution to facilitate the arithmetic)
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