147. Based on data from a dart-throwing experiment, the article “Shooting Darts” (Chance, Summer 1997:

16 –19) proposed that the horizontal and vertical errors from aiming at a point target should be independent of one another, each with a normal distribution having mean 0 and variance s2. It can then be shown that the pdf of the distance V from the target to the landing point is

a. This pdf is a member of what family introduced in this chapter?

b. If s  20 mm (close to the value suggested in the paper), what is the probability that a dart will land within 25 mm (roughly 1 in.) of the target?

f 1v2 

v s2 # ev2/2s2 v 0