Answered: A population of values has a normal…

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.5: Comparing Sets Of Data

Problem 13PPS

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A population of values has a normal distribution with μ=240.1 and σ=82.8. A random sample of size n=33 is drawn. What is the mean of the distribution of sample means ? What is the standard deviation of the distribution of sample means?

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

Expert Solution

Step 1

$\mathrm{\mathbf{given}:}$

$\mathrm{Population\;mean\;(\mu)=240.1 }$

$\mathrm{Population\;standard\; deviation\;(\sigma)=82.8}$

$\mathrm{Sample\;size\;(n)=33}$

The mean of the distribution of sample means is given by

$\mathrm{\mu_{\bar x} =\mu}$

$\mathrm{\mu_{\bar x} =\mathbf{{\color{Red} 240.1}}}$

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