Let x_{1}, x_{2}, . . . , x_{100} denote the actual net weights (in pounds) of 100 randomly selected bags of fertilizer. Suppose that the weight of a randomly selected bag has a distribution with mean 50 lb and variance 1 lb^{2}. Let be the sample mean weight (n = 100).

(a) What is the probability that the sample mean is between 49.85 lb and 50.15 lb? (Round the answer to four decimal places.) P(49.85 ≤ ≤ 50.15) =

(b) What is the probability that the sample mean is less than 50 lb?