Calculating $P(X-E(X)\geq \mathrm{SD})$ for a normal random variable $X$

Question

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.

Answer 1

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