Question Type 3: Finding the probability values of normally distributed variables Exercises

Determine $P(-1.5 < X < 0.5)$ when $X \sim N(0,1)$.

Calculate $P(X > 12)$ for $X \sim N(10,2)$.

Calculate $P(26 < X < 34)$ when $X \sim N(30,4)$.

Find $P(3 < X < 5)$ if $X \sim N(4.5,1.5)$.

Find $P(40 < X < 60)$ if $X \sim N(50,10)$.

Find $P(X < 15)$ for $X \sim N(20,5)$.

Compute $P(X > 125)$ for $X \sim N(100,15)$.

Find $P(X < 3.6)$ if $X \sim N(5,0.8)$.

If $X \sim N(8,3)$, determine $b$ so that $P(X < b) = 0.90$.

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

Let $X \sim N(100,20)$. Find $c$ such that $P(X > c) = 0.05$.

For $X \sim N(0,2)$, determine $d$ so that $P(-d < X < d) = 0.80$.