A bond has an average return of 6.8 percent and a standard deviation of 4.6 percent. What range of returns would you expect to see 68 percent of the time?

a. 2.2 percent to 11.4 percent
b. 4.6 percent to 11.4 percent
c. 4.6 percent to 22.8 percent
d. 11.4 percent to 22.8 percent
e. 11.4 percent to 16.0 percent

hi

To calculate the range of returns that you would expect to see 68 percent of the time, you can use the concept of standard deviation. Since the average return is 6.8 percent and the standard deviation is 4.6 percent, you would expect to see returns within one standard deviation of the average return in approximately 68 percent of the cases.

The range can be calculated by adding and subtracting one standard deviation from the average return.

Lower range = Average return - 1 * Standard deviation
Lower range = 6.8 - 1 * 4.6
Lower range = 6.8 - 4.6
Lower range = 2.2 percent

Upper range = Average return + 1 * Standard deviation
Upper range = 6.8 + 1 * 4.6
Upper range = 6.8 + 4.6
Upper range = 11.4 percent

Therefore, the range of returns that you would expect to see 68 percent of the time is from 2.2 percent to 11.4 percent.

The correct answer is option a. 2.2 percent to 11.4 percent.

To determine the range of returns that you would expect to see 68 percent of the time, you can use the empirical rule, also known as the 68-95-99.7 rule.

According to the empirical rule, approximately 68 percent of the data falls within one standard deviation of the mean. In this case, the mean return is 6.8 percent and the standard deviation is 4.6 percent.

To calculate the range, you can add and subtract one standard deviation from the mean.

So, for the given bond, the expected range of returns would be:
Mean - 1 standard deviation = 6.8 - 4.6 = 2.2 percent
Mean + 1 standard deviation = 6.8 + 4.6 = 11.4 percent

Hence, the correct answer is option a. 2.2 percent to 11.4 percent.

In a normal distribution, 68% of the time scores are within μ±1SD (6.8±4.6). You can do the math.

I hope this helps. Thanks for asking.