7.54 Winning at roulette Part b of Example 7 used the central limit theorem to approximate the probability of coming out ahead if you bet $10 on red on each of 40 roulette wheel spins. For each spin, the winnings are

$10 with probability 18/38 and - $10 with probability 20/38. You are interested in the probability of winning at least $100 over the course of the 40 spins.

a. The average winnings per spin need to be at least how much to win at least $100?

b. Use the central limit theorem to determine the approximate probability of winning at least $100.

c. You must win at least how many of the spins to win at least $100?

d. Using the binomial distribution, calculate the exact probability of winning at least $100 in the 40 spins.

How does your answer compare with that of part b?