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

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

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

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

$$x=51.4\ min$$