Customers arrive at an enquiry desk at a constant average rate of 1 every 5 minutes.

(i) State one condition for the number of customers arriving in a given period to be modelled by a Poisson distribution.

Assume now that a Poisson distribution is a suitable model.

(ii) Find the probability that exactly 5 customers will arrive during a randomly chosen 30-minute period.

(iii) Find the probability that fewer than 3 customers will arrive during a randomly chosen 12-minute period.

(iv) Find an estimate of the probability that fewer than 30 customers will arrive during a randomly chosen 2-hour period.