How to estimate random error in a single measurement?

Question

(from Jwan622's post here),

This image was shown, where we've got:

1. 19 samples (n = 19)
2. Mean of 4.4.
3. Sample standard deviation of 2.3 (s = 2.3)

If the standard error of mean from the sample is SE = s / sqrt(n) = 2.3 / sqrt(19), and if I made one more measurement that had a value of 2, what would be the estimation of random error in that single measurement with 95% confidence?

Would that estimation be:

2 +/- (1.96 * [s + SE])?

The reason I ask is that a book here (2016, Morris, Measurement and instrumentation, 2nd edition) claims this is the case, but I was unable to independently verify it anywhere else.