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
. Multiplying this by does reveal the .