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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 is 5.29% 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 29 ​cents.) It can be shown that in 100 roulette plays on​ black/red, the average casino win percentage is normally distributed with mean 5.29% and standard deviation 11​%. 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(x>​0).​(This is the probability that the casino wins​ money.)

​P(x>​0)=___________​(Round to three decimal places as​ needed.)

b. Find ​P(44less than<xless than<15).

​P(4<x<15)=______ ​(Round to three decimal places as​ needed.

)c. Find ​P(x<2).

​P(x<22​)=________​(Round to three decimal places as​ needed.)

d. If you observed an average casino win percentage of 26​%

after 100 roulette bets on​ black/red, what would you​ conclude?

A.The probability of an average casino win percentage of −26% is very​ small, near 0. The casino is losing money.

B.The probability of an average casino win percentage of −26​% is very​ large, near 1. The casino is winning money.

C.The probability of an average casino win percentage of−26% is very​ large, near 1. The casino is losing money.

D.The probability of an average casino win percentage of minus−26% is very​ small, near 0. The casino is winning money.

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