Sample Distribution Quiz1 - No20

Today I am going to solve a simple quiz based on the knowledge we've learned during last few post.

My quiz is like this.

Can you figure out the probability that sample mean which sampled from the normal distribution (MEAN = 10, SD = 10)  is over 11 ?   (Sample number = 50) 

I emphasized before that we can predict population mean from the sample distribution. however, this is an opposite one because we already know the population mean and standard deviation.

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 ]