Chapter 5.2, Problem 37E

Archery. An archer shoots an arrow into a square target 6 feet on a side whose center we call the origin. The outcome of this random experiment is the point in the target hit by the arrow. The archer scores 10 points if she hits the bull’s eye—a disk of radius 1 foot centered at the origin; she scores 5 points if she hits the ring with inner radius 1 foot and outer radius 2 feet centered at the origin; and she scores 0 points otherwise. Assume that the archer will actually hit the target and is equally likely to hit any portion of the target. For one arrow shot, let S be the score. A probability distribution for the random variable S is as follows.

1. a. On average, how many points will the archer score per arrow shot?
2. b. Obtain and interpret the standard deviation of the score per arrow shot.