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. (c) Suppose that you play the game 100 times so that n= 100 . Describe the sampling distribution of x, the mean amount won per game. The sample mean x is approximately normal. What are the mean and standard deviation of the sampling distribution of x? (Round your results to the nearest penny.) mu Subscript x overbar μx equals = −0.05

Answer #1

for above probability of winning =1/38

therefore for a single game:

x | P(x) | xP(x) |
x^{2}P(x) |

35 | 1/38 | 0.921 | 32.237 |

-1 | 37/38 | -0.974 | 0.974 |

total | -0.053 | 33.211 | |

E(x) =μ= | ΣxP(x) = | -0.0526 | |

E(x^{2}) = |
Σx^{2}P(x) = |
33.2105 | |

Var(x)=σ^{2} = |
E(x^{2})-(E(x))^{2}= |
33.208 | |

std deviation= |
σ= √σ^{2} = |
5.7626 |

hence for 100 games

mean μx =-0.0526 ~ -0.05

and standard deviation =σx =5.7626/sqrt(100)=0.58

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