Write a program in \(\mathrm{R}\) that simulates 100 samples of size \(n\) from distributions that are specified below. Let \(T(F)\) correspond to the quantile functional so that \(T(F)=F^{-1}(\alpha)\) where \(\alpha \in(0,1)\) is a specified constant. For each sample compute \(\hat{\theta}_{n}=T(\hat{F})\) where \(\hat{F}\) corresponds to the empirical distribution function, and again where \(\hat{F}\) corresponds to a NORmAL distribution with mean equal to the sample mean, and variance equal to the sample variance. Construct a scatterplot of the pairs of estimated quantiles and overlay a line on the plot that corresponds to the true value of the population quantile in each case. Repeat these calculations for \(\alpha=0.05,0.10\), \(0.25,0.50,0.75,0.90\), and 0.95, and for \(n=10,25,50\) and 100. Describe the behavior found in each of these plots and discuss how the assumption of NORmALITY affects the performance of the estimator based on the NORMAL distribution.