如何执行模拟以在 R 中找到具有给定概率的 z-score (x)

Question

As the title illustrates, I would like to conduct a simulation test. I was given a probability P(L>x)=0.05, and L follows a normal distribution with mean=0, std=100. I was asked to perform some sort of simulation, IDEALLY using a hit-or-miss approach multiple times to do so in order to find an appropriate x. I was not allowed to use qnorm() function. Can you please help me out? Thank you

Answer 1

As we want P(L>x)=0.05, we can create a function that calculates P(L>x)-0.05, and find the x that turns it to 0 (its root) with uniroot :

prob = function(x){
  n = 10000
  L = rnorm(n,0,100)
  sum(L > x)/n - 0.05}

uniroot(prob, c(-400,-50))

Obs: the second argument for uniroot is the arbitrary interval where it'll try to find the root.

This will find a different root every time you run it as L is created inside prob . For better accuracy, you can increase n .