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

For $k>0$: (a)(i) $0.841$, (ii) $0.309$ (b) $a\approx1.64$. For $k<0$: (a)(i) $0.159$, (ii) $0.691$ (b) $a\approx-1.64$. The non-degenerate normal model requires $k\ne0$.

Using standardization to find probabilities

Using standardization to find probabilities

Solution:

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