Over a number of years, the average annual rate of return for Fidelity's International Capital Appreciation mutual fund has been .035 with a standard deviation of .031.Assume annual returns are approximately normally distributed around the average rate.If you use this historical information as the basis for your calculations, the probability that this fund will produce a positive return is:
A).1292
B).8718
C).1571
D).7882
E).8534

Question

Quizplus · Accepted Answer

Given that the distribution of returns is approximately normal and centered around an average (mean) of 0.035 with a standard deviation of 0.031, to find the probability of a positive return, we look for the probability that the return is greater than 0. This is essentially asking for the area to the right of 0 in a normal distribution centered at 0.035. Since 0 is less than one standard deviation away from the mean, a significant portion of the distribution is to the right of 0, indicating a high probability of a positive return. The exact value isn't provided, but option B, with a probability of 0.8718 (or 87.18%), is the most reasonable estimate given the parameters. This reflects the high likelihood of a positive return based on the fund's historical performance.

Over a Number of Years, the Average Annual Rate of Return