The Central Limit Theorem implies the following important ideas in statistics: (FILL IN THE BBLANKS) 1.) When the sample size tends to infinity (a very large sample) the distribution of the sample mean X will be _______________________ distributed. 2.) If the sample size tends to infinity, the sample mean ?? ̅ ________________ the population mean ?. 3.) When the original variable is normally distributed, the distribution of the  sample means will be ______________________ distributed, for any sample size n.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
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Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 20PFA
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The Central Limit Theorem implies the following important ideas in statistics: (FILL IN THE BBLANKS)

1.) When the sample size tends to infinity (a very large sample) the distribution of the sample mean X will be _______________________ distributed.

2.) If the sample size tends to infinity, the sample mean ?? ̅ ________________ the population mean ?.

3.) When the original variable is normally distributed, the distribution of the  sample means will be ______________________ distributed, for any sample size n.

4.) When the distribution of the original variable might not be normal, a sample size of _______________ or more is needed to use a normal distribution to approximate the distribution of the sample means. The larger the sample, the better the approximation will be.

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