In 1994 an insurance company received claims. from 20% of the motorists it had insured.

(a) For a random sample of 14 motorists insured with the company in 1994, find the probability that (i) exactly three claimed on their insurance, (ii) between two and five inclusive claimed on their insurance, (iii) a majority claimed on their insurance.

(b) For a random sample of 90 motorists insured with the company, use an appropriate approximating distribution to determine the probability that at least 25 claimed on their insurance in 1994. (NEAB)