Answer to Question #16413 in Statistics and Probability for Shane Dorms

Question

The organizer of the Montreal International Art Exhibit is trying to determine its optimal operating hours for its next one-day exhibition. Studies have shown that the arrival times at any given exhibition form a normal distribution with the average time that visitors arrive being 3 hours and 36 minutes after doors open, with a standard deviation of 48 minutes.
a) If the organizer sets the opening of the exhibition at 10:00 a.m., at what time would they expect 90% of the visitors to have arrived?
b) If the organizer sets the opening of the exhibition at 9:00 a.m., at what time after the doors open will only 15% of the visitors have arrived?
c) At what time should the organizer open the exhibition if they would like 60% of the visitors to have arrived by noon (12:00pm) so that they can award the first door prize?