The number of telephone calls coming into the central switchboard of an office building follows a...

The number of telephone calls coming into the central switchboard of an office building follows a Poisson process with an average of 4 calls per minute.

a) What is the probability that at least 3 calls will arrive in a given one minute period?

b) What is the probability that at least 20 calls will arrive in a given five minute period?

c) What is the probability that the time from the opening of the switchboard until the first call exceeds 20 seconds?

d) What is the probability that the time from the opening of the switchboard until the 4th call is at most 45 seconds?

e) Find the mean and variance for the waiting time between the opening of the switchboard and the 3rd call.

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orchestra answered 1 year ago

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