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5 December, 16:13

An investment strategy has an expected return of 15 percent and a standard deviation of 9 percent. Assume investment returns are bell shaped. How likely is it to earn a return between 6 percent and 24 percent?

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  1. 5 December, 19:18
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    68% of an investment earning a return between 6 percent and 24 percent.

    Step-by-step explanation:

    The Empirical Rule states that, for a normally distributed random variable:

    68% of the measures are within 1 standard deviation of the mean.

    95% of the measures are within 2 standard deviation of the mean.

    99.7% of the measures are within 3 standard deviations of the mean.

    In this problem, we have that:

    Mean = 15

    Standard deviation = 9

    How likely is it to earn a return between 6 percent and 24 percent?

    6 = 15 - 1*9

    6 is one standard deviation below the mean

    24 = 15 + 1*9

    24 is one standard deviation above the mean

    By the empirical rule, there is a 68% of an investment earning a return between 6 percent and 24 percent.
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