Question about calculating standard errors with BRR replicate weights

I’m analyzing a survey (the PSS) in which each respondent is a school. I’ve been provided with 88 BRR replicate weights which I was hoping to use to calculate the standard error for the sum of enrollments at specific groups of schools (ex: sum of enrollments at each elementary school). I know I can use Stata and other statistical packages to do the calculation, but I was hoping to do it manually so I could understand the method better and check to see if I did the calculation wrong in Stata. Would it be correct to calculate the standard error for sum of elementary school enrollments as the square root of:

[∑r [∑tWt(enrollment)-µ(enrollment)]2]/88
("r" and "t" are meant to be subscripts and 2 is meant to be a superscript--I couldn't get the formatting to work in the post)
where ∑t wt(enrollment) is the sum of the product of replicate weight t and the enrollment at each school t ; μ is the average of ∑t wt(enrollment) across all 88 replicate weights; and r is each of the 88 replicate weights? If that does happen to be correct, what number should I use to find the critical value to construct a 95% confidence interval? Would it be 88 or the sample number of elementary schools?