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Math Help - Standard Deviation

  1. #1
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    Sep 2007
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    Standard Deviation

    Can anyone help me with this question

    Baby Pty Ltd. is planning to launch a new brand of makeup product. Based on market research, if sales are high they can make a profit of $3.4 million per year. If sales are 'so so' they can make a profit of $1.6 million per year. Finally, if sales are low they can lose $0.5 million. The probabilities for the two profit scenarios are 0.64 and 0.13, respectively. Calculate the standard deviation of profit for the product (in $ millions) to 3 decimal places.


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  2. #2
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    Sep 2007
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    StDev

    E(X) = 0.64 * 3.4 + 0.13 * 1.6 + (1- 0.64 - 0.13) * -0.5 = 2.269

    E(X^2) = 0.64 * 3.4 ^ 2 + 0.13 * 1.6 ^ 2 + (1- 0.64 - 0.13) * -0.5 ^2 = 7.7887

    Standard Deviation = (E(X^2) - E(X)^2)^0.5
    Standard Deviation = (7.7887 - 2.269^2)^0.5 = 1.625
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