A study plans to sample randomly 100 government records of farms in Ontario to estimate the mean acreage of farms in that province. Results from an earlier study suggest that 200 acres is a reasonable guess for the population standard deviation of farm size.

(a) Approximate the probability that the sample mean acreage falls within 10 acres of the population mean acreage.

(b) If in reality the population standard deviation is larger than 200, would the probability be larger, or smaller, than you found in (a)?