Problem 3G Suppose you take a sample of size 400 with replacement from your population and find the sample mean. The sampling distribution of the mean will be appromately normal by the CLT. What will be the expectation and standard error? Plot the normal curve with this expectation and SE (you can see online how to make a normal curve in ggplot with a specific mean and sd). Is it ok to use the SE formula with true variance for the rest of the problem Problem 3H Now take 100 samples, each of size 400 with replacement, from your population. Compute all the sample means and draw the histogram of these 100 means. On the histogram, superpose the normal curve from Problem 3G (i.e., draw the curve again, over the histogram). Problem 31 From each of your 100 samples, construct a 95%-confidence interval for the mean of your population. Determine how many of your intervals contain the population mean. One way to do this is to use an ifelse statement that assigns the value 1 if the true pop mean is in the CI and 0 otherwise