Question 3: Suppose the prices of shirts from a brand are uniformly distributed from $6 to $60 dollars. a. Find the mean shirt price from that brand b. Find the variance of the shirt price. c. Find the probability that a randomly chosen shirt has price greater than 40 dollars. d. Suppose that a random sample of 40 shirts are chosen from the brand. Find the approximate distribution of the average price of the shirts in the sample. e. Find the probability that the average price of the selected shirts is greater than 40 dollars. f. Find the probability that the average price of the selected shirt is less than 30 and greater than 20. g. Use R to draw the density curve of X. Adjust the limits of the x and y axis reasonably so that the positive part (> 0) of the pdf curve is completely shown in the plot. Label the axes and the plot reasonably. Include a red vertical line on the plot to indicate the location of the mean of X