Question 1. A professor commutes daily from Clementi Station to his office. The average time for a one-way trip is 24 minutes, with a standard deviation of 3.8 minutes. Assume the distribution of trip times to be normally distributed.
(a) Compute the probability that a trip will take at least 0.5 hour.
(b) If the professor has to be in his office at 8.30 am and he leaves Clementi Station at 8.15 am daily, compute the percentage of the time that he is late for work.
(c) If the professor leaves Clementi Station at 8.05 am daily and coffee is served at staff lounge from 8.20 am until 8.30 am, compute the probability that he misses coffee.
(d) Compute the probability that 2 out of the next 3 trips will take at least 0.5 hour.