Certain components for a revolutionary new sewing machine are assembled by inserting a part of one type (sprotsil) into a part of another type (weavil). Sprotsils have external dimensions which are normally distributed with mean 2.50 cm and standard deviation 0.018 cm. Weavils have internal dimensions which are normally distributed with mean 2.54 cm and standard deviation 0.024 cm. Under suitable pressure, the two types fit together satisfactorily if the dimensions differ by not more than 0.035 cm. Show that, if pairs of parts are chosen at random, the difference D internal dimension of a weavil -external dimension of a sprotsil is distributed with mean 0.04 cm and standard deviation 0.030 cm. Hence show that approximately 42.8% of randomly selected pairs will fit together satisfactorily. Now, if it is known that the internal dimension of a given. weavil is 2.517 cm, what is the probability that a randomly chosen sprotsil will fit this weavil satisfactorily? (AEB)