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.  Prof. Miller ran a marathon.  Given that the mean finis

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

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