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My question is:

If a random variable has a normal distribution, what are the possibilities it will take on a value within one standard deviation of the mean?

How do you approach this? I don't care about the solution, but, rather, how to get to it.

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Hint: You are asking for $\mathrm P(\mu-\sigma\leqslant X\leqslant\mu+\sigma)$, assuming that the distribution of $X$ is normal $N(\mu,\sigma^2)$. But then $X=\mu+\sigma X_0$ where the distribution of $X_0$ is standard normal $N(0,1)$. Hence...

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    Thats all that I got. I have the solutio$n$ though. The solution is really 2F(1) - 1. Actually I think I kinda got it now, thanks!2011-11-11