1. Normal Distribution Many things closely follow a Normal Distribution:
Heights of people
Size of things produced by machines
Errors in measurements
Blood pressure
Marks on a test
We say the data is "normally distributed".

2. But there are many cases where the data tends to be around a central value with no bias left or right, and it gets close to a "Normal Distribution" like this
Normal Distribution

3. The Normal Distribution has:
Symmetry about the center
50% of values less than the mean and 50% greater than the mean

4. Standard Deviation and Probability

5. Key Areas under the Curve
For normal distributions + 1 SD ~ 68% + 2 SD ~ 95% + 3 SD ~ 99.9%

6. Standard Normal probability Distribution
A random variable that has a mean 0 and SD 1 is said to have a standard normal probability distribution.
This particular random variable is designated by the letter Z.
The Z formula is

7. The z score can be defined as the number of SD that a value X is above or below the mean of distribution.
If the value of X is more than mean Z score is …Positive…………
If the value of X is less than mean Z score is Negative……………
If the value of X is equal to mean Z score is ……………

8. In a grocery store, the mean expenditure per customer is Rs with a SD of Rs If a random sample of 50 customer is selected, what is the probability that the sample average expenditure per customer is more than Rs ?

9. 1-A placement company has conducted a written test to recruit people in a software company. Assume that the test marks are normally distributed with mean 120 and SD 50. Calculate the following:
Probability of randomly obtaining scores greater than 200 in this test.
Probability of randomly obtaining a scores greater that is 180 or less.