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23 September, 07:39

The annual return of a well-known mutual fund has historically had a mean of about 10% and a standard deviation of 21%. Suppose the return for the following year follows a normal distribution, with the historical mean and standard deviation. What is the probability that you will lose money in the next year by investing in this fund?

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  1. 23 September, 11:07
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    The probability of losing money in the next year by investing in the fund is the probability of getting any return less than 0%. We will use a z test to find out the probability.

    So our

    Mean = 10%

    SD = 21%

    Hypothesis X<0

    Formula for z value = (X-Mean) / SD

    0-0.1/0.21 = - 0.476

    Look up value in z table

    =0.3192

    31.92%

    The probability that you will lose money in the next year by investing in this fund is 0.3192 or 31.92 %
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