Please show all work 2. (30 pts) A standard roulette wheel in the U. S. has the

Question

Please show all work

2. (30 pts) A standard roulette wheel in the U. S. has the numbers 1 through 36 plus 0 and 00. Of the numbers 1 through 36, 18 are colored red and 18 are colored black. The numbers 0 and 00 are colored green. If a person observes 40 consecutive spins of the wheel, what is the probability that the number of times that the color black occurs is less than or equal to 15? You can assume that results of separate spins are independent so that this probability can be modeled using the binomial distribution. HINT: Model using the binomial distribution to first determine n, , and the values of X. Then use MINITAB to find the required probability. When you provide your answer, be sure to state the values of n and that you used as well as the probability requested. Also, see the hint at the end of this question.

Explanation / Answer

n=40; Probability of black=p=18/38=0.4736 ; P(not black)=0.5264

P( Black less than 15) = Sum ( 40C r *0.4736^r *0.5264^(40-r)) where r varies from 0 to 15 = 0.13752417424

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