Question: In the game of roulette, there are 18 red numbers, 18 black numbers, and 2 green numbers on the wheel. Suppose that a gambler bets on the color red 175 times. We will examine the proportion of times the gambler wins

a) What is the distribution of the sample proportions that are possible?

b) Determine the probability that the gambler will win more than 50% of the time

c) What is the chance that the gambler’s results will lie within 2% of the expected winning percentage?

d) What will be the expected range for the gambler’s winning percentage?

e) What could the casino do to increase the chance that the gambler’s winning percentage will fall within 2% of the expected winning percentage?

f) If we increased the number of plays to 751, that what is the chance that the gambler will win more than 50% of the time?