TITLE: Calculating $P(X-E(X)\geq \mathrm{SD})$ for a normal random variable $X$
QUESTION [1 upvotes]: If you'd have to calculate the following probability of an $X\sim \mathrm{Normal}$: $$P(X-E(X)\geq \mathrm{SD}),$$
how would you calculate it? And if the calculation will be for $4\cdot\mathrm{SD}$, how does it matter?
Thanks in advance.

REPLY [4 votes]: Hint: If $X\sim\mathcal{N}(\mu,\sigma^2)$, then
$$
\frac{X-\mu}{\sigma}\sim\mathcal{N}(0,1).
$$
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