. Prof. Miller ran a marathon. Given that the mean finishing time for all runners was 255 minutes with a standard deviation of 46 minutes and that finishing times were approximately normally distributed, find
(a) the percent of finishers who ran faster than Prof. Miller’s time of 3 hr 30 min.
(b) a time that was the 23rd percentile (23% of finishers were under that time)
(c) the percent of runners who finished between 3 hours and 4 hours
(d) a random sample of 32 runners got a special vitamin supplement right before the race. Their mean time was 4 hr 2 min. What is the probability that a group of 32 runners chosen at random would have a mean time of 4 hr 2 minutes or less?