A population has a mean =80 and a standard deviation =8. find the mean and standard deviation of a sampling distribution of sample means with sample size=64

Without further information, the mean = 80 and the standard error of the mean = SD for a distribution of means.

SEm = SD/√n

To find the mean and standard deviation of a sampling distribution of sample means, we can use the following formulas:

Mean of the sampling distribution (μᵥ):
μᵥ = μ (mean of the population)

Standard deviation of the sampling distribution (σᵥ):
σᵥ = σ / √n (standard deviation of the population divided by the square root of the sample size)

Given:
Mean of the population (μ) = 80
Standard deviation of the population (σ) = 8
Sample size (n) = 64

Let's calculate it step-by-step:

Step 1: Calculate the mean of the sampling distribution (μᵥ):
μᵥ = μ
μᵥ = 80

Therefore, the mean of the sampling distribution is 80.

Step 2: Calculate the standard deviation of the sampling distribution (σᵥ):
σᵥ = σ / √n
σᵥ = 8 / √64
σᵥ = 8 / 8
σᵥ = 1

Therefore, the standard deviation of the sampling distribution is 1.

To find the mean and standard deviation of a sampling distribution of sample means, we can use the formulas:

Mean of sample means (μᵢ) = Mean of population (μ)
Standard deviation of sample means (σᵢ) = Standard deviation of population (σ) ÷ √Sample size (n)

Given that the mean (μ) of the population is 80 and the standard deviation (σ) is 8, and the sample size (n) is 64, we can calculate the mean and standard deviation of the sampling distribution as follows:

Mean of sample means (μᵢ) = 80
Standard deviation of sample means (σᵢ) = 8 ÷ √64 = 8 ÷ 8 = 1

Therefore, the mean of the sampling distribution of sample means (μᵢ) is 80, and the standard deviation (σᵢ) is 1.