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The central limit theorem tells us that for a population with any distribution, the distribution of the sums for the sample means approaches a normal distribution as the sample size increases. In other words, if the sample size is large enough, the distribution of the sums can be approximated by a normal distribution even if the original population is not normally distributed.
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Central limit theorem: Probability being one of the integral parts of statistics, holds a good number of theories and formulas. Central limit theorem is one of the core segments amongst them.
The importance of the central limit theorem stems from the fact that, in many real applications, a certain random variable of interest is a sum of a large number of independent random variables. In these situations, we are often able to use the CLT to justify using the normal distribution. Examples of such random variables are found in almost.
If you have studied probability theory then you would have definitely learned about the central limit theorem. This theorem is used to state those conditions in which the mean of all the random and independent variables is normally distributed. According to this theorem, all the random variables should be distributed identically.
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Central Limit Theorem Pages 108-112 Homework Notification Due Today: Hwk 4.2 Normal CDF and Inverse Normal Assigned: Friday, November 8th Assigned Today: No Assignments were assigned Due Tomorrow: Hwk 4.2 Normal CDF and Inverse Normal Due Tuesday, November 12th Answers are provided so that you can check for understanding.