I am taking a statistics course focused on R and was asked this question about a normally distributed sample of weights:
Use the CLT to approximate the probability that our sample mean estimate is off by more than 2 grams from the population mean.
The answer was given as:
2 * ( 1-pnorm(2/sd(X) * sqrt(12) ) )
I understand why the value is multiplied by 2 (to estimate for a difference greater than 2 and less than -2), but I don't understand where the rest of the equation was derived from. Can someone explain how this equation is able to answer the above question?