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    Finding the Mean, Variance, Standard Deviation of Sampling Distribution of the Sample Mean

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    Suppose that we will take a random sample of size n from population having mean µ and standard deviation σ. For each of the following situations, find the mean, variance, and standard deviation of the sampling distribution of the sample mean:

    (a) µ = 12 , σ = 2.2 , n = 25 (Round your answers of "σ " to 4 decimal places and "σ 2" to 3 decimal places.)
    µ
    σ 2
    σ
    --------------------------------------------------------------------------------

    (b) µ = 510 , σ = .5 , n = 110 (Round your answers of "σ " to 4 decimal places and "σ 2" to 3 decimal places.)
    µ
    σ 2
    σ
    --------------------------------------------------------------------------------

    (c) µ = 5 , σ = .3 , n = 4
    µ
    σ 2
    σ
    --------------------------------------------------------------------------------

    (d) µ = 110 , σ = 1.2 , n = 1,800 (Round your answers of "σ " to 4 decimal places and "σ 2" to 3 decimal places.)
    µ
    σ 2
    σ
    --------------------------------------------------------------------------------

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    Answers

    (a) µ = 12 , σ = 2.2 , n = 25 (Round your answers of "σ " to 4 decimal places and "σ 2" to 3 decimal places.)

    µ = 12
    σ2 = (2.2)2/25 = 0.194
    σ = √0.194 = 0.4405 ...

    Solution Summary

    The standard deviations of sampling distributions of the sample mean is examined.

    $2.19

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