Question

# 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. (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

for above probability of winning =1/38

therefore for a single game:

 x P(x) xP(x) x2P(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(x2) = Σx2P(x) = 33.2105 Var(x)=σ2 = E(x2)-(E(x))2= 33.208 std deviation= σ= √σ2 = 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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