Problem 6 In this problem, we simulate the previous problem using R and ggplot. Suppose our population follows a normal distribution, N(0, 400). Suppose we know the variance of the population of = 400, but do not know its mean / and our goal is to form 90% confidence intervals for /. (a) Set the seed to 135 using set . seed (135). Take 200 random samples of size 400 each. For each sample, construct the 90% confidence interval (DO NOT PRINT THE INTERVALS). (b) Now draw the PMF of G from the previous question using ggplot. There are different ways of doing this, for example you could use geom histogram with a binwidth of 1 and in the density scale. Mark the number of good intervals above (out of 200) that contain the true . You can do this using geom vline. 3 (c) Based on the values of E[G] and standard error of G, is your mark in a surprising place? explain briefly