Computing a 95% confidence interval on the sum of n i.i.d. exponential random variables

F[x_] := 1 - GammaRegularized[n, a*x];

Fi[p_] := InverseGammaRegularized[n, 1 - p]/a;

ci[c_, a_, n_] := {Fi[a, n, (1-c)/2], Fi[a, n, c+(1-c)/2]}

(* Random draw from an exponential distribution given rate param. *)
getGap[a_] := -1/a*Log[RandomReal[]]

betw[x_, {a_, b_}] := Boole[a <= x <= b]

c = .95;
a = 1/.75;
n = 40;
ci0 = ci[c, a, n];
N@Mean@Table[betw[Sum[getGap[a], {n}], ci0], {100000}]

----> 0.94995