A roulette wheel has38 slots. If you bet a dollar on a particular number, you\'l

Question

A roulette wheel has38 slots. If you bet a dollar on a particular number, you'll win $30 if the ball ends up in that slot and $0 otherwise. The wheel is calibrated so that each outcome is equally likely. (A) Let X denote your winnings when you play one. State the probability distribution of X. It has mean 0.789 and standard deviation 4.802. If X is 0 what is the probability? If X is 30 what is the probability?

(B) You decide to play once a minute for a total of 520 time. What is the mean and standard distribution of your sample mean winnings?

(C) Refer to B. Using the central limit theorem, find the probability that this amount of roulette playing, your mean winning is at least a dollar, so that you have lost no money. The probability is what?

Explanation / Answer

A) here probabilty of losing P(X=0)=37/38 (As there are 37 chance out of 38 of losing)

and Probabilty of winning P(X=30)=1/38 (as there are 1 chance out of 38 of winning)

B) mean of  sample mean winnings =0.789

and std deviation=4.802/(520)1/2 =0.2106

C) P(X>1)=1-P(X<1)=1-P(Z<(1-0.789)/0.2106)=1-P(Z<1.002)=1-0.8418=0.1582

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.