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

Find $\mathrm{P}(X > 25)$ for $X \sim \mathrm{N}(20, 3^2)$.

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

Find $P(65 < X < 80)$ for $X \sim N(70, 3^2)$.

Calculate $P(3 < X < 5)$ for $X \sim N(4.5, 1.5^2)$.

Find $P(X>13)$ for $X ∼ N(10,2^2)$.

Calculate $P(X<28)$ for $X\sim N(30,4^2)$.

Determine $P(230<X<260)$ for $X\sim N(250,10^2)$.

Calculate $P(X>18)$ for $X\sim N(15,2.5^2)$.

Find $P(45 \le X \le 60)$ for $X \sim N(50, 5^2)$.

Calculate $P(X<85)$ for $X \sim N(100,15^2)$.

Compute $P(Z>2.33)$ for $Z\sim N(0,1)$.

Determine $P(-1.96<Z<1.96)$ for $Z \sim N(0,1)$.