## Standard Normal Distribution

- Standardization:
- Every distribution can be standardized.

- When we standardize the normal distribution, the result is Standard Normal distribution.
- Lets understand standardization with an example Refer Here for the example done in the class
- Why Standardize:
- Standarization allows us to:
- Compare different normally distributed datasets
- detect normality
- detect outliers
- create confidence intervals
- test hypotheses
- perform regression analysis

- Standarization allows us to:
- Exercise: Try to standardize the following approximate normal distribution Refer Here

## The Central Limit Theorem (CLT)

- The CLT is one of the greatest statistical insights.
- It states no matter what the underlying distribution of the dataset, the sampling distribution of the means would approximate to normal distribution.
- Moreover, the mean of the sampling distribution would be equal to mean of the original distribution & variance would be n times smaller. where n is size of the sample.
- Theorem can be Represented as
- No matter the distribution
- The more samples, closer to the Normal.

- Standard Error: The standard deviation of the distribution formed by the sample means. Standard Error represents the variability of sample means
- Standard error is used in most statistical test because it shows how well you approximated the true mean