Answer to Question #239562 in Statistics and Probability for yeng

Question

1.  Ben has determined that the length of time it takes him to commute from his residence to school is normally distributed with a mean of 45 minutes and a standard deviation of 5 minutes. How much time must he allow if he wishes to be in his first class on time 90% of the time?

Answer 1

Let $X=$ the length of time: $X\sim N(\mu, \sigma^2).$

Given $\mu=45\ min, \sigma=5\ min.$

$$P(X<x)=P(Z<\dfrac{x-\mu}{\sigma})=P(Z<\dfrac{x-45}{5})=0.9$$

$$=P(Z<\dfrac{x-45}{5})=0.9$$

$$\dfrac{x-45}{5}\approx1.2816$$

$$x=51.4\ min$$