Answer to Question #261416 in Statistics and Probability for Raine

Question

Assume that the time a students stays in school is normally distributed with a mean of 5 hours and a standard deviation of 0.5 hours. Every day, Clark Kent stays in school for 5.5 hours. What proportion of students stays less than 5.5 hours

Answer 1

Let $X=$ the time a students stays in school: $X\sim N(\mu, \sigma^2).$

Given $\mu=5, \sigma=0.5.$

$$P(X<5.5)=P(Z<\dfrac{5.5-5}{0.5})=P(Z<1)$$

$$\approx0.841345$$

$84.1345\%$ of students stay less than 5.5 hours.