Question

You are using a Monte Carlo simulation to estimate the area of shape inside a unit square by taking n sample points. How big does n have to be in order for the estimate to be within about ±0.01 of the correct answer?

I believe this has to do with binomial distribution.

Answer 1

p=   50%      
ME=   0.01       
alpha=   5%      
z(a/2)=   z(0.05/2)   =NORMSINV(1-0.05/2)   1.96
          
n = z(a/2)^2*p*(1-p)/ME^2          
n=   1.96^2*0.5*(1-0.5)/0.01^2      
   9604      
   9604      

9604 simulations should be constructed.