A random sample is selected from a population with mean μ = 102 and standard deviation σ = 10. Determine the mean and standard deviation of the x sampling distribution for each of the following sample sizes. (Round the answers to three decimal places.)
(a) n = 12
μ =
σ =
(b) n = 13
μ =
σ =
(c) n = 37
μ =
σ =
(d) n = 70
μ =
σ =
(f) n = 140
μ =
σ =
(e) n = 560
μ =
σ =
Solution :
Given that mean μ = 102 and standard deviation σ = 10
(a) n = 12
The sampling distribution of x is
=> Mean μx = 102
=> standard deviation σx = σ/sqrt(n) = 10/sqrt(12) = 2.887
(b) n = 13
The sampling distribution of x is
=> Mean μx = 102
=> standard deviation σx = σ/sqrt(n) = 10/sqrt(13) = 2.774
(c) n = 37
The sampling distribution of x is
=> Mean μx = 102
=> standard deviation σx = σ/sqrt(n) = 10/sqrt(13) = 1.644
(d) n = 70
The sampling distribution of x is
=> Mean μx = 102
=> standard deviation σx = σ/sqrt(n) = 10/sqrt(70) = 1.195
(f) n = 140
The sampling distribution of x is
=> Mean μx = 102
=> standard deviation σx = σ/sqrt(n) = 10/sqrt(140) = 0.845
(e) n = 560
The sampling distribution of x is
=> Mean μx = 102
=> standard deviation σx = σ/sqrt(n) = 10/sqrt(560) = 0.423
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