Question Type 4: Finding the value of X using inverse normal Exercises

For $X\sim N(8,3^2)$, find the value $a$ such that $P(X>a)=0.75$.

For $Z \sim N(0,1)$, find $z$ such that $P(Z>z)=0.1587$.

Test scores $X \sim N(70, 8^2)$. Find the pass mark $p$ so that only the top $10\%$ of students pass.

For $X\sim N(60,12^2)$, find $g$ such that $P(g<X<75)=0.80$.

For $X\sim N(120,15^2)$, find $k$ such that $P(X<k)=0.025$.

Lifetimes of bulbs $X \sim N(2000, 200^2)$. Find the lifetime $L$ below which $30\%$ of bulbs fail.

Let $Z \sim N(0,1)$. Find $z$ such that $P(-z < Z < z) = 0.95$.

For $X \sim N(100,10^2)$, find $c$ such that $P(X>c)=0.05$.

For $X \sim \text{N}(5, 2^2)$, find values $a$ and $b$ symmetric about the mean so that $P(a < X < b) = 0.80$.

For $X \sim N(8,3^2)$, find $b$ such that $P(X<b)=0.60$.

For $X\sim N(20,4^2)$, find $f$ such that $P(X>f)=0.20$.