4. A company director monitored the number of errors on each page of typing done by her new secretary and obtained the following results:
| No. of errors | 0 | 1 | 2 | 3 | 4 | 5 |
| No. of pages | 37 | 65 | 60 | 49 | 27 | 12 |
- Show that the mean number of errors per page in this sample of pages is 2 .
- Find the variance of the number of errors per page in this sample.
- Explain how your answers to parts (a) and (b) might support the director's belief that the number of errors per page could be modelled by a Poisson distribution.
(1)
Some time later the director notices that a 4-page report which the secretary has just typed contains only 3 errors. The director wishes to test whether or not this represents evidence that the number of errors per page made by the secretary is now less than 2 . - Assuming a Poisson distribution and stating your hypothesis clearly, carry out this test. Use a \(5 \%\) level of significance.
(6)