Refer to Exercise 4.6.

The mean and standard deviation of the probability distribution for the lottery winnings y are μ = 0.20 and σ = 632.45.

Suppose you play the lottery 1 million times. Let ¯y denote your average winnings.

(a) Find the mean and standard error of the sampling 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?