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 ]

Inferential analysis basic-2 - No18

I think,  another fundamental concept of inferential analysis is standard error of the mean.
In order to explain this, I am going use same function I used before.

As you can see the  below, the larger your sample number , the smaller  standard deviation. In other words, the shape of your sample distribution of sample mean will become more normal distribution.

Inferential analysis basic-1 - No17

One of the reasons that we are studying inferential analysis is prediction. In some cases, it is impossible to gather whole data to evaluate data character. For example, it is nonsense if you try to check all the products which are produced in your factory to check data quality management. Instead, we take a certain amount of sample and believe the result of evaluation as if  we took all the population.
How does it possible ?
Today I will briefly introduce two major theories make above sample test reliable.

First things is in line with central limit theorem. I think I've already explained overview of central limit theorem in previous post. One thing I didn't clearly prove was average value.
In other words, as you take a mean of sample data over and over again, your sample average will be the  average of population.

I am going to show you by simple test using R.

I've make a new function to get a mean from normal distribution (mean = 5, sd = 10)

Normal distribution - No16

When it comes to the probability distribution, you might be think two distributions.

• Discrete distribution 
• Continuous distribution

Normal distribution is very popular distribution which is a continuous probability distribution defined by below formula.