Randolph College and Salem College are within 20 miles of each other, and the students at each college frequently date each other. The students at Randolph College are debating how good their dates are at Salem College. The Randolph students have sampled several hundred of their fellow students and asked them to rate their dates from 1 to 5 (in which 1 is excellent and 5 is poor) according to physical attractiveness, intelligence, and personality. Following are the resulting probability distributions for these three traits for students at Salem College:

Physical Attractiveness Probability 1 .27 2 .35 3 .14 4 .09 5 .15 1.00 Intelligence Probability 1 .10 2 .16 3 .45 4 .17 5 .12 1.00 Personality Probability 1 .15 2 .30 3 .33 4 .07 5 .15 1.00 Simulate 20 dates and compute an average overall rating of the Salem students. LO.1