Question

A company gives an aptitude test to potential employees. The scores are normally distributed with mean 250 and S.D 50.What is the probability that a score is selected at random will be Between 230 and 260.

Answer 1

Let $X=$ the score: $X\sim N(\mu, \sigma^2)$

Given $\mu=250, \sigma=50$

$$P(230<X<260)=P(X<260)-P(X\leq 230)$$

$$=P(Z<\dfrac{260-250}{50})-P(Z\leq \dfrac{230-250}{50})$$

$$=P(Z<0.2)-P(Z\leq -0.4)$$

$$\approx0.5792597-0.34457823\approx0.234681$$