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

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

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

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

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

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

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

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

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

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