If $X \sim N(k, k^2)$, find $\mathrm{P}(X 0)$ \(\mathrm{P}\left(X

Question

If $X \sim N(k, k^2)$, find $\mathrm{P}(X > 0)$ $\mathrm{P}\left(X < \frac{k}{2}\right)$ The constant $a$ such that $\mathrm{P}(|X - k| < ak) = 0.9$.

Accepted Answer

(a) (i) $0.841$; (ii) $0.309$; (b) $1.64$.

Using standardization to find probabilities