State, giving your reasons, the distribution which you would expect to be appropriate in describing

(a) the number of heads in ten throws of a penny,

(b) the number of blemishes per square metre of sheet metal. A building has an automatic telephone exchange. The number X of wrong connections in any one day is a Poisson variable with parameter A. Find, in terms of A, the probability that in any one day there will be

(c) exactly three wrong connections,

(d) three or more wrong connections. Evaluate, to three decimal places, these probabilities when 0.5. Find, to three decimal places, the largest value of for the probability. of one or more wrong connections in any day to be at most (L)