Question

Suppose that we will take a random sample of size n from a population having mean µ and standard deviation σ. For each of the following situations, find the mean, variance, and standard deviation of the sampling distribution of the sample mean

(a) µ = 20, σ = 4, n = 21

(b) µ = 567, σ = .8, n = 138

(c) µ = 6, σ = 1.0, n = 6

Answer 1

To find the mean, variance, and standard deviation of the sampling distribution of the sample mean, you use the formulas µx = µ, σx2 = σ2/n, and σx = √(σx2).

Step-by-step explanation:

a. To find the mean of the sampling distribution of the sample mean, we use the formula µx = µ = 20. To find the variance, we use the formula σx2 = σ2/n = 42/21. And to find the standard deviation, we take the square root of the variance, σx = √(σx2) = √(42/21).

b. For this situation, µx= µ = 567, σx2 = σ2/n = 0.82/138, and σx = √(σx2) = √(0.82/138).

c. Using the given values, µx = µ = 6, σx2 = σ2/n = 12/6, and σx = √(σx2) = √(12/6).