Discuss the below:
Q: A university professor keeps records of his travel time while he is driving between his home and the university. Over a long period of time he has found that his morning travel times are approx Normally distributed with a mean of 31 minutes and a standard deviation of 3.0 minutes;his return journey in the evening is similarly distributed but with a mean of 35.5 minutes and a standard deviation of 3.5 minutes.
a) Find the probability that on a typical day he spends more than one hour traveling to and from work.
b) Find the probability that on a given day his morning journey is longer than his evening journey?
c) On what proportion of days is the evening journey more than 5 minutes longer than the morning journey?
d) A new route was recently opened. He has discovered that if he leaves home at 8:30am and uses this new route, on 88% of days he arrives at the university by 9:00am. If the times of travel are still approx Normally distributed with a standard deviation of 3.0 minutes, find the mean time for his morning trip using the new route.