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A $1 bet on a single number on a casino\'s roulette wheel pays $35 if the ball e

ID: 3223662 • Letter: A

Question

A $1 bet on a single number on a casino's roulette wheel pays $35 if the ball ends up in the number slot you choose. Here is the distribution of the payoff X: Each spin of the roulette wheel is independent of other spins. (a) If Sam plans to bet on $40 roulette spins, he needs to win at least $540 to break even. If each win gives him $35, what is the minimum number of wins m he must have? m = b) What are the mean (plusminus 0.0001) and standard deviation (plusminus 0.0001) of X, the number of wins in 540 roulette spins? mu = sigma =

Explanation / Answer

a)

no of spins = 540

let the minimu no of wins be m

amount he wins = 35*m

for break even Sam should win atleast 540 i.e 35*m>= 540 => m >= 540/35 =15.4286

m >=15.4286 i.e m = 16

b)

mean = np = 540*0.974 = 525.96

variance = np(1-p) = 540*0.974*(1-0.974) = 13.67496

standard deviation = variance = 13.67496 = 3.69797