In Problem S13-11 discuss how you might assess the accuracy of the average rating for North-East University students based on only 20 simulated dates.

Problem S13-11

Northern University and North-East University are located near each other, and the students at each university frequently date. The students at Northern University are debating how good their dates are at North-East University. The Northern students have sampled several hundred of their fellow students and asked them to rate their dates from 1 to 5 (where 1 is excellent and 5 is poor) according to physical attractiveness, intelligence, and personality. Following are the resulting probability distributions for these three traits.

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