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

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    2021-10-11T21:31:08+00:00

    Answer:

    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

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