Let X1, X2, . . . , X100 denote the actual net weights of 100 randomly selected 50-lb bags of fertilizer. a. If the expected weight of each bag is 50 and the variance is 1, calculate P(49.9 X50.1) (approximately) using the CLT. b. If the expected weight is 49.8 lb rather than 50 lb so that on average bags are underfilled, calculate P(49.9 X 50.1).

Variation of sample mean: With a population standard deviation of σ , the variation of the sample means is σX´ , which the standard deviation of the sample mean: σX= σ √n But if we don’t know the population standard deviation, σ , we use the sample standard deviation, S, to approximate the population standard deviation, and the variation of sample means becomes the standard error of the sample mean: S SEX= √ n In general, as long as outcomes of each trial are independent and from a fixed population (random & no replacement or large population relative to sample), then variation of sample ratio is inversely proportional to square root of sample size: