A lawyer commutes daily from his suburban home to his office. The average time for a one-way trip is 30 minutes with a standard deviation of 4.2 minutes. Assume the distribution of duration of commute...

A lawyer commutes daily from his suburban home to his office. The average time for a one-way trip is 30 minutes with a standard deviation of 4.2 minutes. Assume the distribution of duration of commute to be normal, (a) what is the probability that the trip will take at least ½ hour? (b) If the office opens at 9:00 am and he leaves his house at 8:45 am daily, what percentage of the time is he late for work? (c) Find the length of time above which we find the slowest 15% of the trips. (d) Find the probability that 2 of the next 3 trips will take at least ½ hour.