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My textbook features the following question/answer example but offers minimal explanation of how it is derived.

The age at which the fan assembly in a new laptop fails is normally distributed with variance, $\sigma^2$. If seven new laptops are used, find $P\{0.8 \le S^2/\sigma^2 \le 1.1 \}$?

The answer given is:

Multiply by $(n-1)$ to get $P\{4.8 \le (n-1) \frac{S^2}{\sigma^2} \le 6.6 \}$. Then somehow this becomes $0.6406 - 0.4303 = .2103$.

I don't understand where $(n-1)$ came from. Also, how did they find $0.6406 - 0.4303 = .2103$?

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$s^2$ is an unbiased estimator and is sum of squares divided by n-1. sigma is just n. to balance them out, you multiply by n-1 –  Inquest Nov 14 '12 at 20:53
    
unbiased estimator of what? –  Imray Nov 15 '12 at 17:21

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