## 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
• 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

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