N<-10000 #Number of times the sampling is repeated
n<-100 #sample size
mu<-5 #True value of the parameter
xbar<-c()
lower<-c()
upper<-c()

for (j in 1:N){
   x<-rnorm(n,mu,1) #generate a sample of size n from Normal(mu,1)
   xbar[j]<-mean(x) #calculate the sample mean
   lower[j]<-xbar[j]-1.96/sqrt(n) #calculate the lower limit of the CI
   upper[j]<-xbar[j]+1.96/sqrt(n) #calculate the upper limit of the CI
   }


m<- (lower<=5 & 5<=upper)
p<-sum(m)/N #the proportion of CI's that contain mu