Question

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
click here to view the standard normal distribution table (page 1).
click here to view the standard normal distribution table (page 2).
(a) construct a probability distribution for the random variable x, the winnings of each spin
(b) determine the mean random variable x. round your results to the nearest penny
(c) suppose that you p 10. describe the sampling distribution of x, the mean amount won per game.
the sample mean x is

Explanation:

Step1: Check sample size condition

According to the Central Limit Theorem, if \(n\geq30\), the sampling distribution of \(\bar{x}\) is approximately normal. Here \(n = 100\geq30\).

Step2: Determine the mean and standard deviation of the sampling distribution

The mean of the sampling distribution of \(\bar{x}\) is \(\mu_{\bar{x}}=\mu=- 0.05\). The standard deviation of the sampling distribution of \(\bar{x}\) is \(\sigma_{\bar{x}}=\frac{\sigma}{\sqrt{n}}=\frac{5.76}{\sqrt{100}} = 0.576\). Since \(n = 100\geq30\), the sampling distribution of \(\bar{x}\) is approximately normal.

Answer:

approximately normal