Question

Tel-Skein is a call centre which fields all queries by customers of a national bank. Calls that are put through to operators who specialise in queries regarding ‘Lost or Stolen Debit Cards’ occur at random at a mean rate of 90 per hour.

(i) What is the probability distribution, including its parameter(s), of the number of calls arriving in this part of the call centre during a two-minute interval? (There is no need to calculate any probabilities in this part of the question).

(ii) Data have been collected on numbers of customers calling this part of the call centre in 100 two-minute periods and are summarised below. Use an appropriate test to investigate whether or not the data are consistent with your answer to part (i). Explain your method and conclusions carefully.

	number of calls arriving in two minutes period
	o	1	2	3	4	5	>=6
frequency	6	21	24	21	15	5	8

(iii)On Sundays, Tel-Skein runs a ‘skeleton-shift’ (i.e. it employs a reduced number of operators). As a result, operators specialising in ‘Lost or Stolen Debit Cards’ also have to field calls regarding ‘Bill Payments’. Calls regarding ‘Bill Payments’ occur at random at a mean rate of 150 per hour.

Assuming the call rate for ‘Lost or Stolen Debit Cards’ is unchanged, what is the probability that, during a one-minute period on Sundays, there will be between 3 calls and 5 calls; and what is the probability that the gap between calls will exceed 30 seconds?

Answer 1