What is the importance of normal distribution in statistics?

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Accepted Answer

Normal distribution is crucial in statistics for modeling real-world phenomena and facilitating inferential statistics.

Central Limit Theorem: Many statistical methods rely on the assumption of normality; as sample sizes increase, the distribution of sample means approaches normality.
Standard Scores: Normal distribution allows for the calculation of z-scores, which help in understanding how far a data point is from the mean in terms of standard deviations.
Statistical Inference: Many statistical tests (e.g., t-tests, ANOVA) assume normality, making it essential for hypothesis testing and confidence intervals.
Natural Phenomena: Many natural phenomena, such as heights, test scores, and measurement errors, tend to follow a normal distribution, making it a useful model.
Quality Control: In manufacturing, normal distribution is used to monitor processes and ensure products meet quality standards through control charts.

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