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

Calculate $P(26 < X < 34)$, given that $X \sim N(30, 4^2)$.

Determine $P(-1.5 < X < 0.5)$.

Find $P(3 < X < 5)$.

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

Find $P(X < 15)$ for $X \sim N(20, 5^2)$.

Find $P(X < 3.6)$ if $X \sim N(5, 0.8^2)$.

Compute $P(X > 125)$ for $X \sim N(100, 15^2)$.

If $X \sim N(8, 3^2)$, determine the value of $b$ such that $P(X < b) = 0.90$.

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

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

Find $P(40 < X < 60)$ given that $X \sim N(50, 10^2)$.

Let $X$ be a normally distributed random variable such that $X \sim N(100, 20^2)$.

Find the value of $c$ such that $P(X > c) = 0.05$.