Question 261280
I am trying to understand The Central Limit Theorem and do not quite understand the meaning where it states "the distribution of the means will be approximately normal."
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Example you have a set 999 people whose weights are normally distributed.
Say it has a mean of 100 lbs with a standard deviation of 8 lbs.
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You decide to randomly break the set into 333 groups of size 3,
Then you weigh each group and find the mean weight of each group.
You list all those sample means and you look at how they are 
distributed.
The Central Limit Theormem says:
1. The mean of those sample means = the mean of the population (100)
2. The standard deviation of those sample means = (the std of the population)
divided by (the square root of the sample size) (8/sqrt(3)).
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The CLT has certain conditions on it but for problem purposes what
I listed are the relevant facts.
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Why is it advantageous to know that a distribution is approximately normal in The Central Limit Theorem? Thank you for your knowledge and help.
If the population is normal, sampling will tell you approximately where
the population mean is and what its standard deviation is.
That is what the CLT guarantees.
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Cheers,
Stan H.