When a trainee typist types a document the number of mistakes made on any one page is a Poisson variable with mean 3, independently of the number of mistakes made on any other page. Use tables, or otherwise, to find, to three significant figures,

(a) the probability that the number of mistakes on the first page is less than two,

(b) the probability that the number of mistakes on the first page is more than four. When the typist types a 48-page document the total number of mistakes made by the typist is a Poisson variable with mean 144.'" Use a suitable approximate method to find, to three decimal places, the probability that this total number of mistakes is greater than 130. (NEAB)