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Can you give an example to denote the working of the central limit theorem?
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Let's consider the population of men who have normally distributed weights, with a mean of $60 \mathrm{~kg}$ and a standard deviation of $10 \mathrm{~kg}$, and the probability needs to be found out.

If one single man is selected, the weight is greater than $65 \mathrm{~kg}$, but if 40 men are selected, then the mean weight is far more than $65 \mathrm{~kg}$.

The solution to this can be as shown below:

$z=(x-\mu) / ?=(65-60) / 10=0.5$
For a normal distribution $\mathrm{P}(\mathrm{Z}>0.5)=0.409$ $z=(65-60) / 5=1$
$P(Z>1)=0.090$
by Gold Status (13,125 points)

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