Answer to Question #55333 in Statistics and Probability for Yomi

Question

At the town fair, you can pay $5 to toss a ring at a set of bottles. If you get a “ringer” on the small mouth bottle, you win $35. If you get a “ringer” on the medium bottle, you win $10. If you get a “ringer” on the large bottle, you get your $5 fee back (that is, you break even). If you miss, you are out the $5 you paid to play. Ryan is a good shot and his probability of getting a ringer on the small, medium, and large bottles is 10%, 10%, and 5%, respectively.
X -$5 $0 $10 $35
P 0.75 0.10 0.10 0.05
a. Find the math expectation of Ryan’s winnings for a single game.
b. Find the math expectation of Ryan’s winnings after 5 games.
c. Find the variance of Ryan’s winnings for a single game.
d. Find the standard deviation of Ryan’s winnings for a single game.
e. Does it pay for Ryan to play this game at the fair?
f. Find the cumulative distribution function of Ryan’s winnings for a single game and draw its graph.