Suppose that 4% of all tax returns are audited. In a group of n tax returns, consider the probability that at most two r
Posted: Wed Jul 13, 2022 5:10 am
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b.
Two gamblers play a version of roulette with a wheel as shown in the file P05_63.xlsx. Each gambler places four bets, but their strategies are different, as explained below. For each gambler, use the rules of probability to find the distribution of their net winnings after four bets. Then find the mean and standard deviation of their net winnings. The file gets you started. Round your answers to two decimal places, if necessary and if your answer is negative value, please enter "minus" sign. a. Player 1 always bets on red. On each bet, he either wins or loses what he bets. His first bet is for $10. From then on, he bets $10 following a win, and he doubles his bet after a loss. (This is called a martingale strategy and is used frequently at casinos.) For example, if he spins red, red, not red, and not red, his bets are for $10,$10,$10, and $20, and he has a net loss of $10. Or if he spins not red, not red, not red, and red, then his bets are for $10,$20,$40, and $80, and he has a net gain of $10. Mean Standard Deviation b. Player 2 always bets on black and green. On each bet, he places $10 on black and $2 on green. If red occurs, he loses all $12. If black occurs, he wins a net $8 (\$10 gain on black, $2 loss on green). If green occurs, he wins a net $50 ( $10 loss on black, $60 gain on green). Mean Standard Deviation
An elevator rail is assumed to meet specifications if its diameter is between 0.98 and 1.01 inches. Each year a company produces 100 , 000 elevator rails. For a cost of $10/σ2 per year the company can rent a machine that produces elevator rails whose diameters have a standard deviation of σ. (The idea is that the company must pay more for a smaller variance.) Each such machine will produce rails having a mean diameter of one inch. Any rail that does not meet specifications must be reworked at a cost of $12. Assume that the diameter of an elevator rail follows a normal distribution. Round your answers to three decimal places, if necessary. a. What standard deviation (within 0.001 inch) minimizes the annual cost of producing elevator rails? You do not need to try standard deviations in excess of 0.02 inch. b. For your answer in part a, one elevator rail in 1000 will be at least how many inches in diameter?
Suppose that 4% of all tax returns are audited. In a group of n tax returns, consider the probability that at most two returns are audited. How large must n be before this probability is less than 0.01 ?