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A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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A random sample is selected from a population with mean μ = 170 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 = 81
(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 = 170 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 =
x
√n
He
= μ
o= =
Vn
13
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:A random sample is selected from a population with mean μ = 170 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 = 81 (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 = 170 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 = x √n He = μ o= = Vn 13 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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