Poisson & Binomial Distributions (Edexcel A Level Further Maths: Further Statistics 1): Exam Questions

The number of calls received by a helpline is modelled by a Poisson distribution with a mean of 2 calls per 5-minute period.

In a randomly chosen 5-minute period, find

(i) the probability that exactly 3 calls are received,

(ii) the probability that at least 4 calls are received.

After an advertising campaign, the helpline manager wants to know whether the mean number of calls has increased.

The number of calls received in a randomly chosen 20-minute period is recorded.

Stating your hypotheses clearly, and using a 5% level of significance, find the critical region for a suitable test.