Problem

A supermarket receives complaints at a mean rate of 6 per week.

(a) State one assumption necessary, in order for a Poisson distribution to be used to model the number of complaints received by the supermarket.

(b) Find the probability that, in a given week, there are

(i) fewer than 3 complaints received by the supermarket,

(ii) at least 6 complaints received by the supermarket.

In a randomly selected week, the supermarket received 12 complaints.

(c) Test, at the 5% level of significance, whether or not there is evidence that the mean number of complaints is greater than 6 per week.

State your hypotheses clearly.

Following changes made by the supermarket, it received 26 complaints over a 6-week period.

(d) Use a suitable approximation to test whether or not there is evidence that, following the changes, the mean number of complaints received is less than 6 per week.

You should state your hypotheses clearly and use a 5% significance level.

(Total for Question 5 is 16 marks)