The number of telephone calls, \(X\), received per hour for Dr Able may be modelled by a Poisson distribution with mean 6 .
Determine \(\mathrm { P } ( X = 8 )\).
The number of telephone calls, \(Y\), received per hour for Dr Bracken may be modelled by a Poisson distribution with mean \(\lambda\) and standard deviation 3 .
Write down the value of \(\lambda\).
Determine \(\mathrm { P } ( Y > \lambda )\).
Assuming that \(X\) and \(Y\) are independent Poisson variables, write down the distribution of the total number of telephone calls received per hour for Dr Able and Dr Bracken.
Determine the probability that a total of at most 20 telephone calls will be received during any one-hour period.
The total number of telephone calls received during each of 6 one-hour periods is to be recorded. Calculate the probability that a total of at least 21 telephone calls will be received during exactly 4 of these one-hour periods.