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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Business

Barnaby

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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Billy Booker · Answer 1

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 %