#  Simulate one random sample of n=25
#  observations from a standard normal
#  distribution

 x <- rnorm(25)
 x

#  Compute the 75-the percentile of
#  the sample

 y <- quantile(x, 0.75)
 y

#  Use a single statement to estimate
#  the 75-th percentile from a simulated
#  sample of 25 observations from a
#  standard normal distribution

 y <- quantile(rnorm(25), 0.75)
 y

#  Collect the estimated 75_th percentiles
#  for 999 additional simulated samples
#  of size 25

 for(i in 1:999) {
  y <- c(y, quantile(rnorm(25), 0.75) )}


#  Construct a histogram

   lab <- "1000 upper quartile estimates (n=25)"
   hist(y, nclass=20, main=lab)

#  Obtain the average of the simulated estimates

  mean(y)

#  Obtain the standard error of the 1000
#  simulated estimates

  sqrt(var(y))

#  Obtain estimates of the lower 2.5-th percentile and
#  and the upper 97.5-th percentile of the distribution
#  of the estimates of the upper quartile of a standard
#  normal distribution for samples of size 25.

   quantile(y, c(0.025, 0.975))

#  Compute the true value of the upper quartile
#  of a standard normal distribution

   qnorm(.75)