MIS 570-DQ 2

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Westcliff University *

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540

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Economics

Date

Apr 3, 2024

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docx

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2

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3.1 Here is given, Win: $35 with probability 1/38 Loss: -$1 with probability 37/38 Single Bet: Take a single roulette bet situation in which a $1 wager is put on a single number. The expected value, or mean, is determined as -0.05. This indicates that, on average, the outcome results in a 5-cent loss per wager. Concurrently, the standard deviation, a measure of the dispersion of conceivable outcomes, approaches $0.95. Mean (µ) Calculation: µ= (35) * (1/38) – (1) * (37/38) µ= 35/38- 37/38 µ – 0.0526 100 Bets: Expanding this research to include 100 similar bets, the average net gain is -$5.26, which is calculated by multiplying 100 by the average of a single bet. Similarly, the standard deviation of net profits over 100 bets is $9.46, calculated as the square root of 100 times the standard deviation of a single bet. µ of 100 beats = 100 * µ of single beat µ of 100 beats ≈ 100 * -0.0526 µ of 100 beats ≈ 100 * -0.0526 µ of 100 beats ≈ - 5.26 Alternatively, the standard deviation of net winnings over 100 bets is computed as follows: The standard deviation of 100 bets equals 100 times the standard deviation of a single bet. The standard deviation of 100 bets is equal to 100 times the standard deviation of a single bet. The standard deviation of 100 bets is around 10 x 0.95. The standard deviation of 100 bets is around 10×0.95. The standard deviation of 100 bets is approximately 9.46. The standard deviation of 100 bets is approximately 9.46.
95% Confidence Interval: Formula= Mean ± 1.96 * Standard Deviation. A confidence interval is used to estimate the expected range of net profits from 100 bets with a 95% confidence level. This interval, using the mean and standard deviation, has an estimated range of -$24.88 to $14.36. Thus, with a 95% confidence level, it is expected that net earnings from 100 bets will fall within this range. Mendenhall, W., Beaver, R. J., & Beaver, B. M. (2016). Introduction to Probability and Statistics. Cengage Learning.
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