If the mean annual return is 4% and the standard deviation is 8%, you would expect 1/3 of annual returns to fall outside a range of:

• A. -4% to +4%
• B. -8% to +8%
• C. -4% to +12%
• D. -12% to +20%

Answer: (C)

The key idea is that about 68% of outcomes fall within one standard deviation of the mean in a normal distribution, leaving roughly 32% outside that range. With a mean of 4% and a standard deviation of 8%, the range spanning one standard deviation is 4% ± 8%, which is -4% to +12%. Since about a third of results are expected outside this interval, that matches the question’s 1/3 figure.

Other ranges don’t line up with that ±1 standard deviation idea. -4% to +4% is centered at 0%, not at the mean of 4%. -8% to +8% is also centered at 0% and isn’t centered on the mean. -12% to +20% is centered on the mean but spans about two standard deviations, which would yield only about 5% outside, not one-third.