Answered: Explain about the Probability of a…

Holt Mcdougal Larson Pre-algebra: Student Edition 2012

1st Edition

ISBN:9780547587776

Author:HOLT MCDOUGAL

Publisher:HOLT MCDOUGAL

Chapter6: Ratio, Proportion, And Probability

Section: Chapter Questions

Problem 5CR

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Question

Explain about the Probability of a Particular Sample Mean.

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Step 1-Introduction

Solution:

Sample mean :

Sample mean is simply the average of all the measurements in the sample. If the sample is random, then the sample mean can be used to estimate the population mean.

Central Limit theorem-

Suppose X is a random variable with a distribution that may be known or unknown with mean= and

standard deviation =

If you draw random samples of size n then as n increases, the random variable which consists of sample means,

is called sampling distribution of sample means.

sampling distribution of the mean approaches a normal distribution as n, the sample size, increases.

That is,

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