structural:expansion, information:extraction
A formula when simulations' results are bounded

An alternate formula can be used in the special case where all simulation results are bounded above and below.

Choose a value for ε that is twice the maximum allowed difference between μ and m. Let 0 < δ < 100 be the desired confidence level, expressed as a percentage. Let every simulation result r, r, … r, … r be such that a ≤ r ≤ b for finite a and b. To have confidence of at least δ that | μ – m | < ε /2, use a value for n such that

n ≥ 2 (b − a) 2 ln (2 / (1 − (δ / 100))) / ϵ 2 {\displaystyle n\geq 2(b-a)^{2}\ln(2/(1-(\delta /100)))/\epsilon ^{2}}

For example, if δ = 99%, then n ≥ 2(b – a) ln(2/0.01)/ ε ≈ 10.6(b – a) / ε.