A candy maker produces mints that have a label weight of 20.4 grams. Assume that the distribution of the weights of these mints is N(21.37, 0.16).
(a) Let denote the weight of a single mint selected at random from the production line. Find P( < 20.857).
(b) During a particular shift, 100 mints are selected at random and weighed. Let Y equal the number of these mints that weigh less than 20.857 grams. Approximate P(Y ≤ 5).
(c) Let Xequalthesamplemeanofthe100mintsselected and weighed on a particular shift. Find P(21.31 ≤ X ≤ 21.39).