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|(X+7)/(14)\right|\le\frac x{14}\right)`

`=\mathbb P\left(|Z|\le\frac x{14}\right)=0.44`

`\implies\mathbb P\left(-7\le Z\le\frac x{14}\right)=0.22`

`\implies\mathbb P\left(Z\le\frac x{14}\right)=0.5+0.22=0.72`


`\implies\frac x{14}\approx0.5828`

`\implies x\approx8.1598`