Question 6 - A-Level Maths

The number of emails per hour received by a helpdesk were recorded. The results for a random sample of 80 one-hour periods are shown in the table.

Number of emails per hour	0	1	2	3	4	5	6
Frequencies	1	10	23	15	19	9	3

Show that the mean number of emails per hour in the sample is 3 The manager believes that the number of emails per hour received could be modelled by a Poisson distribution. The following table shows some of the expected frequencies.
Number of emails per hour Expected Frequencies
0 \(r\)
1 11.949
2 17.923
3 17.923
4 13.443
5 \(s\)
\(\geqslant 6\) \(t\)
Find the values of \(r , s\) and \(t\), giving your answers to 3 decimal places.
Using a 10\% significance level, test whether or not a Poisson model is reasonable. You should clearly state your hypotheses, test statistic and the critical value used.