Tutorial Exercise A random sample is selected from a population with mean = 160 and standard deviation 13. Determine the mean and standard deviation of the sampling distribution of x for each of the following sample sizes. (a) n-4 (b) n=14 (c) n = 64

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Tutorial Exercise
A random sample is selected from a population with mean μ = 160 and standard deviation = 13. Determine the mean and standard deviation of the sampling distribution of x for each of the following sample sizes.
(a) n = 4
(b) n = 14
(c) n = 64
(d) n = 125
(e) n = 169
(f) n = 500
Step 1
(a) n = 4
We are given that a random sample is selected from a population with mean μ = 160 and standard deviation = 13. We are asked to determine the mean and standard deviation of the sampling distribution of the sample mean, X, for the sample size n = 4.
Recall the general properties of the sampling distribution x. The mean is μ = μ, and the standard deviation is
=
σ--
H= = μ
13
0
√n
We can use these formulas to make the desired calculations, rounding a result to three decimal places if it is not exact.
Transcribed Image Text:This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part. Tutorial Exercise A random sample is selected from a population with mean μ = 160 and standard deviation = 13. Determine the mean and standard deviation of the sampling distribution of x for each of the following sample sizes. (a) n = 4 (b) n = 14 (c) n = 64 (d) n = 125 (e) n = 169 (f) n = 500 Step 1 (a) n = 4 We are given that a random sample is selected from a population with mean μ = 160 and standard deviation = 13. We are asked to determine the mean and standard deviation of the sampling distribution of the sample mean, X, for the sample size n = 4. Recall the general properties of the sampling distribution x. The mean is μ = μ, and the standard deviation is = σ-- H= = μ 13 0 √n We can use these formulas to make the desired calculations, rounding a result to three decimal places if it is not exact.
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