Exercise 3.72. In a lumberjack competition a contestant is blindlblded and spun around 9 times. The blindfolded contestant then tries to hit the target point in the middle of a hurizontai log with an axe. The contestant receives 15 points if his hit is within 3 cm of the target, it] points if his hit is between 3 cm and to cm of? the target, I O ' 5 points if his hit is between 10 cm and 20 em off the target, and II zero points if his hit is 20 em or more away from the target {and someone may lose a nger\". Let Y record the position of the hit, so that Y = y :1 0 corresponds to missing the target point to the right by 3: cm and Y = y z: 0 corresponds to missing the target to the left by y em. Assume that Y is normally distributed with mean it = O and variance lOO emz. Find the expected number of points that the contestant wins