This is a question in S2 which is at the start of learning Normal distribution topic BEFORE we have gone onto modelling discrete situations.
The question is about catching a bus which leaves at set times. How do I work these out.
Here is the question.
Each weekday a man goes to work by bus. His arrival time at the bus stop is Normally distributed with standard deviation 3 minutes. His mean arrival time is 8:30am. Buses leave promptly every five minutes at 8:21am, 8:26am, etc. Find the probabilities that he catches the bus at 8:26am.
Because there are sort of time slots I wasn't sure how to calculate this.
My attempt was:
Normalise time to minutes. Eg 8:26am = 506 minutes.
z = (506 - 510) / 3 = -4/3 = -1.3 recurring
use +ve value so phi(1.333) = 0.9087
So P(8:26am) = 1 - 0.9087 = 0.0913
Book answer is 0.0900. Yes I know its close but sure I am not calculating correctly. So how do I calculate in this situation???