4.31. Refer to Exercise 4.6. The mean and standard devi- ation of the probability distribution for the

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4.31. Refer to Exercise 4.6. The mean and standard devi- ation of the probability distribution for the lottery winnings y are 0.10 and 316.23. Suppose you play the lottery 1 million times. Let y denote your average winnings.

(a) Find the mean and standard error of the sam- pling distribution of y.

(b) About how likely is it that you would "come out ahead," with your average winnings exceeding $1, the amount you paid to play each time?

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