## Elementary Statistics (12th Edition)

Published by Pearson

# Chapter 6 - Normal Probability Distributions - 6-5 The Central Limit Theorem - Beyond the Basics - Page 296: 25

#### Answer

a) $μ=6$ $σ=2.16$ b) 4,5 ; 4.5 5,5; 5 9,5; 7 5,9; 7 4,9;6.5 9,9; 9 4,4; 4 4,9; 6.5 c) $1.08$ d) The result is the same as in part c).

#### Work Step by Step

a) We find that the mean is: $μ=\frac{4+5+9}{3}=6$ We know the following equation for the standard deviation: $σ=\sqrt{\frac{Σ(x−\overline{x})^2}{n}}$ Using the proper values, $σ=2.16$. b) We take into consideration all the possible samples: Sample; mean 4,5 ; 4.5 5,5; 5 9,5; 7 5,9; 7 4,9;6.5 9,9; 9 4,4; 4 4,9; 6.5 c) We find that the mean is: $\overline{μ}=6$ We use the equation $σ=\sqrt{\frac{Σ(x−\overline{x})^2}{n}}$, in which $n=6$, to find that the standard deviation is equal to $1.080$. d. We plug in the known values into $σ=\sqrt{n}\sqrt{\frac{N-n}{N-1}}$ to get a value of 1.08. This is the same as the value that we found in part c).

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