Editing Monte Carlo method (section)

==== A formula when simulations' results are bounded ====
An alternative formula can be used in the special case where all simulation results are bounded above and below.

Choose a value for <math>\epsilon</math> that is twice the maximum allowed difference between <math>\mu</math> and <math>m</math>. Let <math>0 < \delta < 100</math> be the desired confidence level, expressed as a percentage. Let every simulation result <math>r_1, r_2, \ldots, r_i, \ldots, r_n</math> be such that <math>a \leq r_i \leq b</math> for finite <math>a</math> and <math>b</math>. To have confidence of at least <math>\delta</math> that <math>|\mu - m| < \epsilon/2</math>, use a value for <math>n</math> such that:

:<math>n\geq 2(b-a)^2\ln(2/(1-(\delta/100)))/\epsilon^2</math>

For example, if <math> \delta = 99\% </math>, then <math>n \geq 2(b - a)^2 \ln(2/0.01)/\epsilon^2 \approx 10.6(b - a)^2/\epsilon^2</math>.<ref name=":1" />