Let x 1 , x 2 , , x 100 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 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

Question: Let x 1 , x 2 , . . . , x 100 denote the actual weights (in pounds) of 100 randomly selected bags of

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 x̅ 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?

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