Four Friends Are Contemplating Joining a Local Bowling League

Short Answer

Four friends are contemplating joining a local bowling league. Let X₁,X₂,X₃,X₄ be the score of the first, second, third, and fourth friend, respectively, on a randomly chosen game. From past experience, the friends know that: E(X₁ )=110, E(X₂ )=125, E(X₃ )=113, and E(X₄ )=140. Additionally, σ₁=7, σ₁=13, σ₁=10, and σ₁=20. Define their total score on a randomly chosen game as Y=X₁+X₂+X₃+X₄. Assume the four players' scores are independent.
-Calculate σ_Y.