People who play the carnival game Lucky Ducks pick a plastic duck from among those floating in a small pool. Each duck has a value written on the bottom that determines the prize. Most say “Sorry, try...

People who play the carnival game Lucky Ducks pick a plastic duck from among those floating in a small pool. Each duck has a value written on the bottom that determines the prize. Most say “Sorry, try again!” Otherwise, 25% pay $1, 15% pay $5, and 5% pay $20. Let the random variable
 denote the winnings from picking a duck at random.

a. Graph the probability distribution of
.
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b. Estimate the mean of Y from the graph of its probability distribution.⁶

c. Find the expected value of Y. What’s your interpretation of the mean if the carnival charges $2 to play this game?
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