Question Type 1: Using properties of normal distribution to find probabilities given some value Exercises

Let $X \sim \text{N}(0,1)$. Find the value of $a$ such that $\text{P}(X > a) = 0.3$.

Let $X \sim N(0,1)$. Given $P(X < a)=0.05$, find $P(X > -a)$.

Let $X\sim N(0,1)$. Compute $P\bigl(|X| > 2\bigr)$.

Let $X\sim N(2,4)$. Find the value $a$ such that $P(X > a) = 0.3$.

Let $X \sim N(5,16)$. Find $a$ such that $P(X > a) = 0.025$.

In a population of adult heights, $X\sim N(170,6^2)$. What is the probability that a randomly chosen adult is taller than 172 cm?

Let $X \sim N(50, 16)$. Find $a$ such that $P(X > a) = 0.84$.

Let $X \sim N(100, 25)$. If $P(X > a) = 0.1$, find $P(X < 200 - a)$.

Let $X\sim N(3,1)$. If $P(X > a)=0.3$, calculate $1 - P\bigl(X < 4 - a\bigr)$.

Let $X\sim N(10,4)$. Find $c$ such that $P(10 - c < X < 10 + c)=0.95$.

Let $X \sim N(10, 9)$. Find the value $a$ such that $P(X < a) = 0.8$.

Let $X \sim N(0,1)$. Given $P(X > 1.3)=p$, express $P(X < -1.3)$ in terms of $p$.