A population has a mean of 100 and a standard deviation of 15. For samples of size 25, find the mean and standard error of the sampling distribution of the sample mean.

Step 1: Find the mean of the sampling distribution.

The mean of the sampling distribution of the sample mean equals the population mean.

Therefore:
μ_x̄ = μ = 100

Step 2: Recall the standard error formula.

The standard error of the sample mean is:
SE = σ / √n

Step 3: Identify the values.

σ = 15
n = 25

Step 4: Substitute into the formula.

SE = 15 / √25

Step 5: Simplify.

√25 = 5

SE = 15 / 5
SE = 3

Therefore, the sampling distribution has a mean of 100 and a standard error of 3.