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).(a) Fill in the probability distribution table for random variable X, the winnings of each spin:x P(x)35 ___-1 ___(b) Determine the mean and standard deviation of the random variable X. (round to nearest penny).Mean = ?SD = ?(c) Suppose that you play the games 80 times so that n = 80. Describe the sampling distribution of x-bar, the mean amount won per game. The sample mean is skewed left, skewed right, or approximately normal? Answer is .What are the mean and standard deviation of the sampling distribution of x-bar? (round to nearest penny)Mean = ?SD = ?(d) What is the probability of being ahead after playing the game 80 times? That is, what is the probability that the sample mean is greater than 0 for n = 80? (round to four decimal places as needed).(e) What is the probability of being ahead after playing the game 240 times? (round to four decimal places as needed).(f) What is the probability of being ahead after playing the game 800 times? (round to four decimal places as needed).(g) Compare results of parts (d) through (f). What lesson does this teach you?A) The probability of being ahead decreases as the number of games played increases. B) The probability of being ahead decreases as the number of games placed decreases. C) The probability of being ahead increases as the number of games played increases. D) The probability of being ahead remains the same as the number of games played varies.

a) $ 9.50

b) 17

c) y-intercept (0, 12). this is the initial amount of money that joe had prior to playing any game.

d) x-intercept ( 24, 0). this is the number of games that joe will play before he depletes the initial amount of money that he had.

e) slope is -0.5. joe's balance will reduce by 0.5 for every game that he plays.

f)

domain; [0,24]

range; [0,12]

g) x + 2y = 24

step-by-step explanation:

a)

if joe plays 5 games, this will imply that x = 5. substitute x = 5 in the equation and solve for y;

y = -.50x + 12

y = -0.50(5) + 12

y = 9.50

b)

if joe leaves the arcade with $3.50, this will mean that y = 3.50. plug in y = 3.50 in the given equation and solve for x;

y = -.50x + 12

3.50 = -0.50x + 12

0.50x = 12 - 3.50

0.5x = 8.5

x = 17

c)

the function given is   y = -.50x + 12.

the y-intercept is the point where the graph of this function will intersect the y-axis. at this point, the value of x is usually 0. plug in x = 0 in the given equation and determine y;

y = -0.50(0) + 12

y = 12

the y-intercept is thus (0, 12). this is the initial amount of money that joe had prior to playing any game.

d)

the x-intercept refers to the point where the graph of a function intersects with the x-axis. at this point, the value of y is 0. substitute y = 0 in the given equation and solve for x;

0 =   -.50x + 12

0.5x = 12

x = 24

x-intercept ( 24, 0). this is the number of games that joe will play before he depletes the initial amount of money that he had.

e)

the slope of the given equation is -0.5. the equation has been given in slope-intercept form. thus the slope is simply the coefficient of x.

joe's balance will reduce by 0.5 for every game that he plays. this is the interpretation of the slope.

f)

domain is the set of x values for which the function is real and defined. the domain will thus be; [0,24]. this will restrict the balance to only assume positive values.

on the other hand, the range is the set of y values for which a function is real and defined. the range in our case will be [0,12]. joe can have between $0 and $12 balance.

g)

the standard form of the equation of a straight line is;

ax + by = c

where a, b, and c are integers.

our equation is given as;

y = -.50x + 12

re-writing the equation we have;

0.5x + y = 12

divide all through by 0.5;

x + 2y = 24

a

step-by-step explanation:

answer: i literally just answered this question but they want me to do it again

step-by-step explanation: