A lawyer commutes daily from his suburban home to his midtown office. The average time for a one-way trip is 24 minutes, with a standard deviation of 3.8 minutes. Assume the distribution of the trip-length to be normally distributed.

a. If the office opens at 9:00am and he leaves his house at 8:40 am daily, what percentage of the time is he late for work? You must draw the distribution and indicate the relevant numbers etc. You must also give the answer as a number.
b. Find the length of time above which we find the longest 20% of the trips. You must draw the distribution and indicate the relevant numbers etc. You must also give the answer as a number.
c. Find the probability that two of the next three trips will take at least 30 minutes.