Answer to Question #281468 in Statistics and Probability for JAY

Question

The average travel time from your residence to your school is 35 minutes with a standard deviation of 10 minutes. If you want to be 99% certain that you will not be late for first 9:00 am class, what is the latest time you should leave home? Assume that the time travel is normally distributed

Answer 1

$$P(Z<z)=0.99$$

$$z\approx2.3263$$

$$z=\dfrac{x-\mu}{\sigma}$$

$$\dfrac{x-35}{10}\approx2.3263$$

$$x=2.3263(10)+35$$

$$x=58.263 \ min$$

$$9\ hours-58.263\ min=8hours\ 1.737\ min$$

The latest time you should leave home is $8:02.$