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Skiing: Steve Austin is a world class Olympic skier. In his favorite event 'the slalom' the goal is to ski down the 1km hill as fast as possible going the correct way around each of 20 posts without falling. With the new rules, either falling or going the wrong way around one of the posts will cost him the race.
Naturally, Steve is an excellent skier and will get around the posts in the correct direction 98% of the time, he rarely falls, about three time on his last nine trips through the course, and if he completes the race, his completion time is normally distributed with an average of 120 seconds and a standard deviation of 2 seconds.
a. What is the probability he makes it down the hill without falling?
b. What is the probability that he will get through all the gates in the correct direction?
c. Assuming he is the last skier to go and the best time so far is 118 seconds, what is the chance he will win the race?
At western university the historical mean of scholarship exam scores for freshman applications is 900. A historical population standard deviation = 180.
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