Specify a suitable model for the distribution of \(X\).
Find the mean and the standard deviation of \(X\).
\item A secretarial agency carefully assesses the work of a new recruit, with the following results after 150 pages:
\end{enumerate}
No of errors
0
1
2
3
4
5
6
No of pages
16
38
41
29
17
7
2
Find the mean and variance of the number of errors per page.
Explain how these results support the idea that the number of errors per page follows a Poisson distribution.
After two weeks at the agency, the secretary types a fresh piece of work, six pages long, which is found to contain 15 errors.
The director suspects that the secretary was trying especially hard during the early period and that she is now less conscientious. Using a Poisson distribution with the mean found in part (a), test this hypothesis at the \(5 \%\) significance level.