Sam and Mary are salespeople. Sam’s weekly sales X is uniformly distributed: X U[1, 5] (in thousands of dollars).

Sam and Mary are salespeople. Sam’s weekly sales X is uniformly distributed: X ∼ U[1, 5] (in thousands of dollars). Mary’s sales Y follows normal distribution with mean µ = 3 and standard deviation σ = 1.3: Y ∼ N (3, 1.3 2 ). Each week they compare their performance by the ratio X/Y . If ratio X/Y < 0.3, Sam buys the dinner; if ratio X/Y > 0.7, Mary buys; otherwise, they split the check. Assume sample size N = 200 weeks. How often will Sam buy the dinner, how often will Mary buy, and how often will they split?