Answer to Question #261402 in Statistics and Probability for Ayana Prica

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 your first 8:00 am class, what is the latest time you should leave home? Assume that travel time is normally distributed.

Answer 1

Solution:

$P(Z<z)=0.99.$

$\Rightarrow z=2.326$ [Using z-score table]

$\Rightarrow \frac{x-35}{10}=2.326$

$\Rightarrow x=2.325\times10+35=58.25$

The latest time you should leave home: $8:00-58.25=7:01.75\approx7:02.$