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 of the target, 5 points if his hit is between 10 cm and 20 cm of the target, and Zero points if his hit is 20 cm or more away from the target. 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 Y=-y<0 corresponds to missing the target to the left by y cm. Assume that Y is normally distributed with mean mu=0 and variance 100 cm2. Find the expected number of points that the contestant wins.
Unitary Method
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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 of the target,
- 5 points if his hit is between 10 cm and 20 cm of the target, and
- Zero points if his hit is 20 cm or more away from the target.
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 Y=-y<0 corresponds to missing the target to the left by y cm. Assume that Y is
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