In a Las Vegas casino, gamblers lose a mean of $0.18 on each roulette game, with a standard deviation of $3.44. (Since the standard deviation is quite high with respect to the mean, roulette players often win money on a bet.) Suppose a gambler plays roulette for 200 bets straight. What is the probability that he will be winning after 200 bets? (Hint: He is winning when the amount of his total earnings is positive.)
Carry your intermediate computations to at least four decimal places. Report your result to at least three decimal places.