Question: The blanks are to be machined to the component profile. The machining equipment can only accept blanks which are no more than 120mm wide and 500mm long.

The probability of the length being greater than 500mm is 2.5% (0.025) and the probability of the width being greater than 120mm is 3% (0.03).

(a) Calculate the probability of a blank being oversize in both dimensions.

(b) Show that the probability that a blank is unacceptable (i.e. is oversize in either dimension) is 0.05425.

(c) Use the binomial distribution to find the probability that two blanks selected at random from a sample of six will be oversize, if the probability of a blank being oversize in either dimension is 0.05425.

(d) Use the Poisson distribution to find the probability that two blanks selected at random from a box of 20 will be oversize, using p = 0.05425 as above