Thanks in advance. Here is a problem that is bugging me. I believe I have come to the correct answer but unfortunatley the answer isn't provided in my Professor's lecture.

Assume that your drive time to work each morning follows a normal distribution with μ = 20 min 24 sec, and σ = 5 min 12 sec. You should be at work by 8 AM. If it takes 3 minutes to get from your car to your office, at what time should you leave home if you want the probability of being late to be ≤ 0.05? Hint Convert to Secs.

Using Normsinv function I received a Z-score of -1.645.

=1224-(312x-1.645)

1737.24 + 180 = 1917.24 comes out rounded 32 min 7:28am.

Is that even close to being on track for this type of problem.