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).
(a) Fill in the probability distribution table for random variable X, the winnings of each spin:
x P(x)
------------------
35 ___
-1 ___
(b) Determine the mean and standard deviation of the random variable X. (round to nearest penny).
Mean = ?
SD = ?
(c) Suppose that you play the games 80 times so that n = 80. Describe the sampling distribution of x-bar, the mean amount won per game.
The sample mean is skewed left, skewed right, or approximately normal? Answer is ________.
What are the mean and standard deviation of the sampling distribution of x-bar? (round to nearest penny)
Mean = ?
SD = ?
(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 n = 80? (round to four decimal places as needed).
(e) What is the probability of being ahead after playing the game 240 times? (round to four decimal places as needed).
(f) What is the probability of being ahead after playing the game 800 times? (round to four decimal places as needed).
(g) Compare 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 increases.
B) The probability of being ahead decreases as the number of games placed decreases.
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.