A supermarket receives complaints at a mean rate of 6 per week.
State one assumption necessary, in order for a Poisson distribution to be used to model the number of complaints received by the supermarket.
Find the probability that, in a given week, there are
fewer than 3 complaints received by the supermarket,
at least 6 complaints received by the supermarket.
In a randomly selected week, the supermarket received 12 complaints.
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.
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.