Four Friends Are Contemplating Joining a Local Bowling League

Multiple Choice

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.
-The friends decide it would only be worth it to join the bowling league if they could average a total score of 500. Should they join the league?

A) Yes, since their expected total score is greater than 500.
B) No, since their expected total score is less than 500.
C) Yes, since it is possible for their total score to be greater than 500 on a randomly chosen game.
D) No, since it is not possible for their total score to be greater than 500 on a randomly chosen game.