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Question: casino games of pure chance eg craps roulette baccarat and...

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Casino games of pure chance​ (e.g., craps,​ roulette, baccarat, and​ keno) always yield a​ "house advantage." For​ example, in the game of​ double-zero roulette, the expected casino win percentage is5.37% on bets made on whether the outcome will be either black or red.​ (This implies that for every​ $5 bet on black or​ red, the casino will earn a net of about 37 ​cents.) It can be shown that in 100 roulette plays on​ black/red, the average casino win percentage is normally distributed with mean 5.37% and standard deviation 10%. Let x represent the average casino win percentage after 100 bets on​ black/red in​ double-zero roulette. Complete parts a through d.

a. Find ​P(xgreater than>​0). ​(This is the probability that the casino wins​ money.)

​P(xgreater than>​0)=_____________​(Round to three decimal places as​ needed.)b. Find

b. ​P(5 less than<xless than<16).

​P(5 less than<xless than<16)=_______​(Round to three decimal places as​ needed.)

c. Find ​P(x less than <1​).​P(x less than<11​)=__________​(Round to three decimal places as​ needed.)

d. If you observed an average casino win percentage of −23​% after 100 roulette bets on​ black/red, what would you​ conclude?

A.The probability of an average casino win percentage of −23% is very​ small, near 0. The casino is winning money.

B.The probability of an average casino win percentage of −23% is very​ small, near 0. The casino is losing money.

C.The probability of an average casino win percentage of −23% is very​ large, near 1. The casino is winning money.

D.The probability of an average casino win percentage of −23% is very​ large, near 1. The casino is losing money.

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