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    Quantitative Methods Homework

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    Hello,

    Here are three quantitative methods problems.

    Thanks!

    --------------------------------

    Prob 1

    Bill and Joe are playing a match in which the first player to win 2 games wins the match. For any given game, the probability that Bill wins is 1/3.

    (a) Find the probability that Bill wins the match.
    (b) What is the probability that the match takes only 2 games?

    Prob 2

    If the mean of a distribution is 100 and the standard deviation is 20, what is the range (+/- x) of the middle 3% of the population if we assume it is normal?

    Prob 3

    Demand (D) is often expressed as a function of price (P). Given the following demand curve, at what price will demand = 10?
    D = 5000 - 25P - P^3

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    https://brainmass.com/statistics/normal-distribution/quantitative-methods-homework-180966

    Solution Preview

    PROBLEM 1

    Here are the possible ways the match can turn out. B means that Bill won the game; J means that Joe won the game.

    B B Bill wins in 2.
    B J B Bill wins in 3
    B J J Joe wins in 3.
    J B B Bill wins in 3.
    J J Joe wins in 2.
    J B J Joe wins in 3.

    Find the probabilities of each scenario by multiplying by 1/3 if Bill wins the game or by 2/3 if Joe wins.

    B B Bill wins in 2. Probability: 1/3 * 1/3 0.1111
    B J B Bill wins in 3 1/3 * 2/3 * 1/3 0.0741
    B J J Joe wins in 3. 1/3 * 2/3 * 2/3 0.1481
    J B B Bill wins in 3. 2/3 * 1/3 * 1/3 0.0741
    J J Joe wins in 2. 2/3 * 2/3 0.4444
    J B J Joe wins in 3. 2/3 * 1/3 * 2/3 0.1481

    Notice that the probabilities add up to 1 (100%).

    Find the ...

    Solution Summary

    The expert examines quantitative methods in probability.

    $2.19

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