I do not know how to begin solving this, it is a multi question problem and I apologize for how long the questons are. I have several for homework, but I think if someone can explain what I need to do, I will be able to complete the rest on my own. If this is too long, I would appreciate any help you can offer. Thank you for your time.
Playing Roulette: A roulette wheel in Las Vegas has 38 slots. If you bet a dollar on a particular number, you'll win $35 if he ball ends up in that slot and $0 otherwise. Roulette wheels are calibrated wo that each outcome is equally likely.
a. Let Xdenote your winnings when you play once. State the probability distribution of X. (This also represents the population distribution you would get if you could play roulette an infinite number of times.) It has mean 0.921 and standard deviation 5.603.
b. You decide to play once a minute for 12 hours a day for the next week, a total of 5040 times. Show that the sampling distribution of your sample means winnings has a mean =0.921 and standard error =0.079.
c. Refer to (b). Using the central limit theorem, find the probability that with this amount of roulette playing, your mean winningsis at least $1, so that you have not lost money after this week of playing. (Hint: Find the probability that a normal random variable with mean 0.921 and standard deviation 0.079 exceeds 1.0)
Playing Roulette: A roulette wheel in Las Vegas has 38 slots. If you bet a dollar on a particular number, you'll win $35 if he ball ends up in that slot and $0 otherwise. Roulette wheels are calibrated wo that each outcome is equally likely.
a. Let Xdenote your winnings when you play once. State the probability distribution of X. (This also represents the population distribution you would get if you could play roulette an infinite number of times.) It has mean 0.921 and standard deviation 5.603.
b. You decide to play once a minute for 12 hours a day for the next week, a total of 5040 times. Show that the sampling distribution of your sample means winnings has a mean =0.921 and standard error =0.079.
c. Refer to (b). Using the central limit theorem, find the probability that with this amount of roulette playing, your mean winningsis at least $1, so that you have not lost money after this week of playing. (Hint: Find the probability that a normal random variable with mean 0.921 and standard deviation 0.079 exceeds 1.0)
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