Question

Random samples of size n were selected from populations with the means and variances given here. Find the mean and standard deviation of the sampling distribution of the sample mean in each case. (Round your answers to four decimal places.)

(a) n = 64, μ = 15, σ2 = 9
find σ and μ

Answer 1

The mean of the sampling distribution of the sample mean is 15 and the standard deviation is 0.375 in this case.

Step-by-step explanation:

In this case, we have a random sample of size n = 64 taken from a population with a mean of μ = 15 and a variance of σ^2 = 9. To find the mean of the sampling distribution of the sample mean, we use the formula μ_x = μ, which means the mean of the sampling distribution is equal to the population mean. Therefore, the mean of the sampling distribution in this case is 15.

To find the standard deviation of the sampling distribution of the sample mean, we use the formula σ_x = σ / sqrt(n), where σ is the population standard deviation and n is the sample size. Plugging in the values, we get σ_x = 3 / sqrt(64) = 3/8 = 0.375. Therefore, the standard deviation of the sampling distribution in this case is 0.375.