Define the Poisson distribution and state its mean and variance. The number of telephone calls received at al switchboard in any time interval of length T minutes has a Poisson distribution with mean T. The operator leaves the switchboard unattended for five minutes. Calculate to three decimal places the probabilities that there are

(a) no calls,

(b) four or more calls in her absence. Find to three significant figures the maximum length of time in seconds for which the operator could be absent with a 95% probability of not missing a call. (NEAB)