Chapter 8, Problem 33CR

Let x₁, x₂, …, x₁₀₀ denote the actual 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 pounds and variance 1 pound². Let $\bar{x}$ be the sample mean weight (n = 100).

1. a. Describe the sampling distribution of $\bar{x}$．
2. b. What is the probability that the sample mean is between 49.75 pounds and 50.25 pounds?
3. c. What is the probability that the sample mean is less than 50 pounds?