In a call centre, the number of telephone calls, \(X\), received during any 10 -minute period follows a Poisson distribution with mean 9
Find
\(\mathrm { P } ( X > 5 )\)
\(\mathrm { P } ( 4 \leqslant X < 10 )\)
The length of a working day is 7 hours.
Using a suitable approximation, find the probability that there are fewer than 370 telephone calls in a randomly selected working day.
A week, consisting of 5 working days, is selected at random.
Find the probability that in this week at least 4 working days have fewer than 370 telephone calls.