A Roulette wheel has 38 numbers, 18 RED, 18 BLACK, and 2 GREEN. If you bet $1 on

Question

A Roulette wheel has 38 numbers, 18 RED, 18 BLACK, and 2 GREEN. If you bet $1 on black and win you make a profit of $1. Consider a gambler who makes a sequence of $100 bets on Black.

a) If he makes 5 independent $100 bets what is the probability that he will end up with a profit?

b) Starting with $500, he makes 5 $100 bets. What is the probability that he doubles his money?

c) Starting with $50,000, if he makes 500 $100 bets, what is the probability that he will end up with a profit?

d) Starting with $50,000 if he makes 500 $100 bets, what is the probability that he will end up with a profit of at least 5%

e)Starting with $50,000 if he makes 500 $100 bets, how many times should he plan on paying so that he has at least a 10% chance of showing a profit?

2) You take a sample of 100 observations from a population with known  and compute a 95% confidence interval based on your data. If you repeat this procedure 1000 times would it be unusual if only 900 of the intervals contained the true mean? justify your answer by a calculation and explain HOW unusual it would be.

3) Suggest an appropriate number of surveys to estimate the difference between 2 proportions with a margin of error equal to 3%. Assume you are going to do this by sending out surveys to the 2 groups (Men and Women) and assume that women have a 30% nonresponse rate and men have 40% nonresponse rate. Specifically: suggest how many surveys should be sent out to each group.

Explanation / Answer

One question for one post 2) You take a sample of 100 observations from a population with known µ and compute a 95% confidence interval based on your data. If you repeat this procedure 1000 times would it be unusual if only 900 of the intervals contained the true mean? justify your answer by a calculation and explain HOW unusual it would be. We are going to find the 95% confidence interval based on your data proportion of the mean contained in the interval is 0.9 z(a/2) = 1.96 from the standard normal with 95% confidence. 0.9-1.96*sqrt(0.9*0.1/1000) , 0.9-1.96*sqrt(0.9*0.1/1000) 0.9- 0.0186 , 0.9+0.0186 0.8814 . 0.9186

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