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?

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 %