The time of departure of my train from Temple Meads Station is distributed normally about the scheduled time of 08:25 with a standard deviation of 1 minute. I arrive at Temple Meads. Station on another train whose time of arrival is normally distributed about the scheduled time of 08:20 with standard deviation of 1 minute. It takes me three minutes to change platforms. If I miss the train from Temple Meads, I am late for work.

(a) Find the probability that I am late for work.

(b) Find the probability that I miss the train from Temple Meads Station every day from Monday to Friday in a given week.