Practice Central Limit Theorem Proof - Tutorial

Practice Central Limit Theorem Proof - Definition, Tutorial, Formula, Example

Definition:

Central limit theorem is a fundamental theorem of probability and this theorem states that the distribution of the sum of a larger number of independent and equally distributed variables will be approximately normal, irrespective of the fundamental distribution.

Formula :
Sample mean ( μx ) = μ Sample standard deviation ( σx ) = σ / √ n
where,
μ=Population mean σ=Population standard deviation n=Sample size
Example:

Find out the standard deviation, if the sample size, population mean and standard deviation are 30,25,50

Given,

Sample Size (n) = 30 Population mean (μ) = 25 Population standard deviation (σ) = 50

To Find,

Sample mean

Solution:
Step 1 :

Substitute the given values in the Sample mean formula,

Sample mean ( μx ) = μ = 25

To Find,

Sample standard deviation

Solution:

Substitute the given values in the standard deviation formula,

Step 1 :

Sample standard deviation ( σx ) = σ / √ n =50 / √ 30 = 50 / 5.47 = 9.13

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