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 different 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 in order 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 in order 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?