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Given a standard deviation of 20, and a mean of 75, how many samples are required...

Given a standard deviation of 20, and a mean of 75, how many samples are required for the mean to be normally distributed regardless of true distribution? Using central limit theorem.
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Answer #1

We have given mean () = 75 and standard deviation () = 20

Central Limit Theorem : The central limit theorem states that the sampling distribution of the sample means approaches a Normal distribution as the sample size gets larger ,no matter what the shape of the population distribution. This fact hold especially true for sample sizes over 30.

In other words we can say that as you take more samples (>= 30) especially large ones, your graph of the sample means will look more like a Normal distribution.

Hence for given a standard deviation of 20, and a mean of 75, 30 ( greater than or equal to 30) samples are required for the mean to be normally distributed regardless of true distribution.

Hope this will help you. Thank you :)

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