1 )

You finally take a break from work and explore the casino! In the game of roulette, a wheel consists of 38 slots numbered 0, 00, 1, 2,..., 36. To play the game, a metal ball is spun around the wheel and is allowed to fall into one of the numbered slots. If the number of the slot the ball falls into matches the number you selected, you win $35; otherwise you lose $1.

A.Construct a probability distribution for the random variable X, the winnings of each spin.

B.Determine the mean and standard deviation of the random variable X. Round your results to the nearest penny.

C.Suppose that you play the game 70 times so that n = 70. What are the mean and standard deviation of the sampling distribution of the sample mean? Round your results to the nearest penny.

D.What is the probability of being ahead after playing the game 70 times? That is, what is the probability that the sample mean is greater than 0 for n = 70?

E.What is the probability of being ahead after playing the game 210 times?

F.What is the probability of being ahead after playing the game 700 times?

G.Compare the results of parts (d) through (f). What lesson does this teach you?

2)

However, you cannot break yourself a way from work.There is a plebiscite coming up in the 2022 state election, where residents are going to vote on making gambling illegal in the state of Jefferson. Curious if you believe it will win, you take random sample of 1023 adults at the Casino asking "Do you think gambling should remain legal or will you vote for the upcoming measure?" Of the 1023 adults surveyed, 725 indicated that they believe gambling should remain legal in Jefferson. Complete parts (a) through (e) below.

A.Obtain a point estimate for the population proportion of adults in the state who believe that gambling should remain legal.

B.Construct and interpret a 95% confidence interval for the population proportion of adults in the state who believe gambling should remain legal.

C.Is it possible that a supermajority (more than 60%) of adults in the state that plan to vote in favor of the plebiscite (to make gambling illegal in Jefferson)? Is it likely?

D.Use the results of part (c) to construct a 95% confidence interval for the population proportion of adults in the state who believe that gambling should be illegal.

E.What confounding factors may be occurring in this study that may mean you have not taken a representative sample of the state?