- The number of errors made by a secretary is modelled by a Poisson distribution with a mean of 2.4 per 100 words.
A 100-word piece of work completed by the secretary is selected at random.
- Find the probability that
- there are exactly 3 errors,
- there are fewer than 2 errors.
After a long holiday, a randomly selected piece of work containing 250 words completed by the secretary is examined to see if the rate of errors has changed.
- Stating your hypotheses clearly, and using a \(5 \%\) level of significance, find the critical region for a suitable test.
- Find P (Type I error) for the test in part (b)