4. A centre for receiving calls for the emergency services gets an average of \(3 \cdot 5\) emergency calls every minute. Assuming that the number of calls per minute follows a Poisson distribution,

1. find the probability that more than 6 calls arrive in any particular minute. Each operator takes a mean time of 2 minutes to deal with each call, and therefore seven operators are necessary to cope with the average demand.
2. Find how many operators are required for there to be a \(99 \%\) probability that a call can be dealt with immediately. It is found from experience that a major disaster creates a surge of emergency calls. Taking the null hypothesis \(\mathrm { H } _ { 0 }\) that there is no disaster,
3. find the number of calls that need to be received in one minute to disprove \(\mathrm { H } _ { 0 }\) at the \(0.1 \%\) significance level.