# 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

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