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 5.385.38%

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 3838

cents.) It can be shown that in 100 roulette plays on black/red, the average casino win percentage is normally distributed with mean 5.385.38%

and standard deviation 1111%.

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)equals=nothing

(Round to three decimal places as needed.)

b. Find P(44less than1515).

P(44less than1515)equals=nothing

(Round to three decimal places as needed.)

c. Find P(xless than<22).

P(xless than<22)equals=nothing

(Round to three decimal places as needed.)

d. If you observed an average casino win percentage of minus2323%

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

A.

The probability of an average casino win percentage of minus2323%

is very large, near 1. The casino is winning money.

B.

The probability of an average casino win percentage of minus2323%

is very large, near 1. The casino is losing money.

C.

The probability of an average casino win percentage of minus2323%

is very small, near 0. The casino is losing money.

D.

The probability of an average casino win percentage of minus2323%

is very small, near 0. The casino is winning money.