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In: Statistics and Probability

In the game of​ roulette, a wheel consists of 38 slots numbered​ 0, 00,​ 1, 2,...,...

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. Complete parts ​(a) through ​(g) below

(a) Construct a probability distribution for the random variable​ X, the winnings of each spin. x ​P(x)

​(Type integers or decimals rounded to four decimal places as​ needed.) ​

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

muequals negative 0.05 sigmaequals 5.76

​(c) Suppose that you play the game 80 times so that nequals80. Describe the sampling distribution of x overbar​, the mean amount won per game.

The sample mean x overbar is approximately normal. skewed right. skewed left. approximately normal. What are the mean and standard deviation of the sampling distribution of x overbar​? Round your results to the nearest penny. mu Subscript x overbarequals 0.003 sigma Subscript x overbarequals 0.644 ​

(d) What is the probability of being ahead after playing the game 80 ​times? That​ is, what is the probability that the sample mean is greater than 0 for nequals80​? ​P(x overbargreater than​0)equals 0.3566 ​(Type an integer or decimal rounded to four decimal places as​ needed.)

​(e) What is the probability of being ahead after playing the game 240 ​times? ​P(x overbargreater than​0)equals nothing ​(Type an integer or decimal rounded to four decimal places as​ needed.) ​

(f) What is the probability of being ahead after playing the game 800 ​times? ​P(x overbargreater than​0)equals nothing ​(Type an integer or decimal rounded to four decimal places as​ needed.)

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

A. The probability of being ahead decreases as the number of games played decreases.

B. The probability of being ahead decreases as the number of games played increases.

C. The probability of being ahead increases as the number of games played increases.

D. The probability of being ahead remains the same as the number of games played varies.

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Expert Solution

orchestra answered 2 years ago
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