[email protected] wrote:What does it mean by being one standard deviation from the mean

It means (mean - standard deviation) or (mean + standard deviation)

[email protected] wrote:A certain characteristic in a large population has a distribution that is symmetric about the mean m. If 68 percent of the distribution lies within one standard deviation d of the mean, what percent of the distribution is less than m + d ?

For a better understanding visualize the situation on a number line as follows...

<---------(m - d)--------m--------(m + d)---------->

As the data is symmetric about m, m is exactly middle point of the distribution.

Now 68% of the distribution lies within one standard deviation d of the mean.
Hence, (m - d) to (m + d) = 68% of the distribution.
So, m to (m + d) = (68/2)% = 34% of the distribution.

Hence, percentage of distribution less than (m + d) = 50% + 34% = 84%

The correct answer is D.