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 pounds and variance 1 pound 2. Let x ̅ be the sample mean weight (n = 100).

a. Describe the sampling distribution of x ̅.

b. What is the probability that the sample mean is between 49.75 pounds and 50.25 pounds?

c. What is the probability that the sample mean is less than 50 pounds?