Suppose that 2500 customers subscribe to a telephone exchange. There are 80 trunklines available. Any one customer has the probability of .03 of needing a trunkline on a given call. Consider the situation as 2500 trials with probability of success p=.03, what is the approximate probability that the 2500 customers will tie-up the 80 trunklines at any given time?
You can use binomial distribution, when the problem satifies the 4 characteristics listed below :
. The experiment consists of n identical trials
. Each trial results in 1 of 2 outcomes called 'success' and 'failure'
. P('success') = p remains constant from trial to trial, and p('failure') = 1-p
. Each trials is independent, i.e. not affected by results of other trials.
This characteristics perfectly suits the problem that you brought up therefore i think it is best to use binominial distribution to solve the problem. If i am not wrong u need to find th z-score and use a table for get the answer. Remember to apply the continuity correction for these kind of problem. Hope it helps.