10 UConn men vs Ivy League Since the 198081 season the UConn

10. UConn men vs. Ivy League Since the 1980–81 season, the UConn men’s basketball team has played 31 games against Ivy League opponents, only losing two games (both to Yale in Dec. 1986 and Dec. 2014). Here are some relevant statistics:

Random Variable Meaning Mean St. Dev. X Points scored by UConn per game 75 15 Y Points scored by Ivy League opponent per game 57 12 Also X and Y are not independent: the correlation between X and Y is 5 8 . (a) Show via explicit computation that the standard deviation of X Y is 12. [Useful: 122 = 144 and 152 = 225.] (b) By the central limit theorem, the distribution of X Y can be approximated by a normal distribution with mean 75 57 = 18 and standard deviation 12. Use this to approximate P[X Y < 0], the probability that UConn loses to an Ivy League opponent in a typical matchup

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Solution