Empirical Rule - No19

This post will guide you how to interpret normal distribution.
We will be able to use normal distribution in order to  predict population mean, so we have to understand the major characteristics of normal distribution.

I think, I already mentioned about "Z score" but today I will explain more about this.
What is Z-Score means ?
Z-score means,  how many standard deviations are away from the mean.
Therefore, Z-score is calculated by below formula.



I explained how to calculate probability in accordance with Z score in post number 16.

Interesting thing is,
As you can see below, there is empirical rule which is very useful to calculate the percentage.

We called this as empirical rule of normal distribution.
If your distribution is normally distributed following rule is applied.
one standard deviation between the mean is occupied 68.2% of the total.
and two stand deviation between the mean is occupied 95.4 of the total.
and third one is occupied 99.6
Someone say this rule is 68.2/95.5/99.6 rule.



[ Normal distribution is defined by   μ = 0 and σ = 1 ]





We already know another important rule to decide standard deviation of sample mean.



This rule explains that if your sample size is so huge, then your standard deviation of sample mean has low value relatively. In other words, your sample mean which is  calculated by huge sample size are very close to a population mean.

Bell shaped curve will be more center centric like this.
And we can also expect that  smaller standard deviation can cause a higher percentage (confidence) of the sample mean.




In conclusion, if you want to get a result with a  better confidence interval, more sample size is required.