The built-in dataset DNase data frame has 176 rows and 3 columns of data obtained during development of an ELISA assay for the recombinant protein DNase in rat serum. The data for this problem can be found in this built-in R dataset under the density column. Let the random variable X represent a random observation from DNase$density. Assume these values are a random sample from a population with distribution X. Assume X has mean mu and standard deviation sigma. Answer the following using R code. Give the R code to assign the data of DNase$density column to the vector x Calculate the sum of the elements of x. Calculate the sum of the squares of the elements of x. Calculate the mean of x, call this mean xbar. Calculate the 65th percentile of x. Calculate an unbiased estimate for the mean of X. Calculate an unbiased estimate of the variance of X. Calculate the critical value to be used to produce an 85% confidence interval for mu. Find the lower boundary for an 85% confidence interval for mu. Find the upper boundary for an 85% confidence interval for mu. Copy your R script for the above into the text box here