Arriving time of a Normal Variable. What is the correct procedure? **I'm stuck in how to salve this problem:** The length of time X (in minutes) it takes to go from your home to donwtown is normally distributed with μ = 30 minutes and X = 5 minutes. What is the latest time that you should leave home if you want to be over 99% sure of arriving in time for a job interview taking place in downtown at 2pm? I was thinking on using that the 99% is 3 standard deviation from the mean, but I can not reach the correct answer 1.18pm. **Question: I need to know the procedure to salve this kind of exercises. Thanks!**

Look at a table of the standard normal. The "$3$ standard deviation units" is not right. We have $\Pr(Z\le 2.33)\approx 0.99$.

Since $\sigma=5$, with probability $0.99$ our travel time will be $\le 30+(5)(2.33)$, so we should leave about $30+(5)(2.33)$ minutes before the appointment.