Kinda, what you have here is a one sample CI for a mean.

If n is small you have a problem.

And I do not know if this SD is the sample st dev, known as s or the population sd, known as .

If its s the correct CI is...

.

where we are assuming normality of our sample.

And if we do know , then the correct CI is...

.

where we are assuming normality of our sample, or approximating via the Central Limit Theorem.

Now , so if we take the second interval here and subract the lower limit from the upper limit

we have...

. Multiplying this by does reveal the .