According to the empirical rule, what proportion of bond mutual funds are expected to have returns within $1^{\sigma }$ of the mean if the returns are approximately normally distributed?

• A. $68\%$
• B. $95\%$
• C. $50\%$
• D. $99.7\%$

Answer: (A)

Verified step by step guidance

1. Understand that the empirical rule applies to data that is approximately normally distributed and describes the percentage of data within certain standard deviations from the mean.
2. Recall the empirical rule states: about 68% of data falls within one standard deviation of the mean, about 95% within two standard deviations, and about 99.7% within three standard deviations.
3. Identify that the problem asks for the proportion of bond mutual funds with returns within one standard deviation of the mean, which corresponds to the first part of the empirical rule.
4. Express this proportion as a percentage, which is approximately 68%.
5. Conclude that according to the empirical rule, about 68% of bond mutual funds are expected to have returns within one standard deviation of the mean.