Question

Suppose that X ∼ N(−7, 14). Find the value of x for which P(|X + 7| ≤ x) = 0.44

Answer 1

$\mathbb P(|X+7|\le x)=\mathbb P\left(\left|\dfrac{X+7}{14}\right|\le\dfrac x{14}\right)$
$=\mathbb P\left(|Z|\le\dfrac x{14}\right)=0.44$
$\implies\mathbb P\left(-7\le Z\le\dfrac x{14}\right)=0.22$
$\implies\mathbb P\left(Z\le\dfrac x{14}\right)=0.5+0.22=0.72$

$\implies\dfrac x{14}\approx0.5828$
$\implies x\approx8.1598$