In one part of the country, one person in 80 has blood of Type P. A random sample of 150 blood donors is chosen from that part of the country. Let X represent the number of donors in the sample having blood of Type P.

(a) State the distribution of X. Find the parameter of the Poisson distribution which can be used as an approximation. Give a reason why a Poisson approximation is appropriate.

(b) Using the Poisson distribution, calculate the t probability that in the sample of 150 donors at least two have blood of Type P.

(c) A hospital urgently requires blood of Type P. How large a random sample of donors must be taken in order that the probability of finding at least one donor of Type P should be 0.99 or more. (MEI)