In Olympic speed-skating, two Americans called Bob and Joe are competing. Their results are normally distributed, with means of 120 and 121 seconds and standard deviations of 3 and 5 seconds, respectively. The fastest non-American skater (i. e., among everyone except Bob and Joe) records a time of 118 seconds (the fastest time wins, of course).
(a) Sketch the distribution of Bob's results, and show graphically (with numbers added) how likely he is to finish at least second?
(b) How likely is it that an American wins the gold medal?
(c) How likely is it that Americans win both the gold and the silver?