In: Statistics and Probability
Let x1, x2, . . . , x100 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 30 lb and variance 1 lb2. Let x be the sample mean weight (n = 100).
(a) What is the probability that the sample mean is between 29.85 lb and 30.15 lb? (Round your answer to four decimal places.) P(29.85 ≤ x ≤ 30.15) =
(b) What is the probability that the sample mean is less than 30 lb?