Problem

A traffic expert claims that the number of breakdowns occurring each day on a busy section of a motorway follows a Poisson distribution with mean $0.7$. The number of breakdowns each day over a 200-day period was recorded. The following table contains the observed frequencies together with some of the expected frequencies using the expert’s distribution.

Number of breakdowns per day	0	1	2	3	4	$\ge 5$
Observed frequency	88	73	26	7	3	3
Expected frequency	99.317	$m$	24.333	5.678	0.994	$n$

(a) Find the value of $m$ and the value of $n$, correct to 3 decimal places.

(b) Carry out a goodness of fit test at the 5% significance level to investigate the expert’s claim.