Exercise 3.72. in a lumberjack competition a contestant is blindfolded and spun around 9 times. the blindfolded contestant then tries to hit the target point in the middle of a horizontal log with an axe. the contestant receives 15 points if his hit is within 3 cm of the target, 10 points if his hit is between 3 cm and 10 cm off the target, 5 points if his hit is between 10 cm and 20 cm off the target, and zero points if his hit is 20 cm or more away from the target (and someone may lose a let y record the position of the hit, so that y = y > 0 corresponds to missing the target point to the right by y cm and y = −y < 0 corresponds to missing the target to the left by y cm. assume that y is normally distributed with mean μ = 0 and variance 100 cm2. find the expected number of points that the contestant wins.