## 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

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.

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2 weeks 2021-10-11T21:29:41+00:00 1 Answer 0

The mean  of a sampling distribution of sample means is 87

The standard deviation of a sampling distribution of sample = 4

Step-by-step 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