6. A lawyer commutes daily from his suburban home to his midtowno?ce. The average time for a one-way trip is 24 minutes, with astandard deviation of 3.8 minutes. Assume the distribution of thetrip-length to be normally distributed. (a) If the o?ce opens at9:00am and he leaves his house at 8:40 am daily, what percentage ofthe time is he late for work? You must draw the distribution andindicate the relevant numbers etc. You must also give the answer asa number. (b) Find the length of time above which we ?nd thelongest 20% of the trips. You must draw the distribution andindicate the relevant numbers etc. You must also give the answer asa number. (c) During a period of 20 work days, on how many daysshould you expect the lawyer to be late for work? (d) What is theprobability that he is late on at most 10 of those 20 days?
