## The following is R code to verify the results in HW 8 Problem 2.b  with that of Problem 3.b. 


# Choose large enough n for CLT to be a reasonable approximation and suppose we observe \bar{X} = 20 
n<-900 
x_bar <- 20 

# Lower bound of exact CI for \tau  
x_bar/qgamma(0.025, shape=n,rate=n, lower.tail=T)  

# Lower bound of approximate CI for \tau 
x_bar/(1+(qnorm(0.025, lower.tail=T)/sqrt(n)))