Question

A population has a mean mu μ equals = 87 and a standard deviation σ = 24. Find the mean and standard deviation of a sampling distribution of sample means with sample size n equals = 36 mu μx equals = nothing (Simplify your answer.) sigma Subscript x overbar σx equals = nothing (Simplify your answer.

Answer 1

The mean of a sampling distribution of sample means is 87

The standard deviation of a sampling distribution of sample = 4

Explanation:

* Lets revise some definition to solve the problem

- The mean of the distribution of sample means is called μx

- It is equal to the population mean μ

- The standard deviation of the distribution of sample means is

called σx

- The rule of σx = σ/√n , where σ is the standard deviation and n

is the size of the sample

* lets solve the problem

- A population has a mean (μ) is 87

∴ μ = 87

- A standard deviation of 24

∴ σ = 24

- A sampling distribution of sample means with sample size n = 36

∴ n = 36

∵ The mean of the distribution of sample means μx = μ

∵ μ = 87

∴ μx = 87

* The mean of a sampling distribution of sample means is 87

∵ The standard deviation of a sampling distribution of sample

means σx = σ/√n

∵ σ = 24 and n = 36

∴ σx = 24/√36 = 24/6 = 4

* The standard deviation of a sampling distribution of sample = 4