5. Use it commander to explore the distribution of the sample mean i when the 1irariatlle of interest it follows an extremer skewed distribution. The data file "Samplenileanjxponential" contains three columns: [i] Column 1 {x}: 1.000 observations from an exponential distribution with mean in [rate=i .f 1o=o.i }. A histogram of this column approximates the shape at the population distribution. [2] Column 2 [xbann]: sample means at LOUD samples of size n=5 generated from an exponential distribution with mean in. A histogram of this column 4 STAT 15] Assignment 3 Total: it): marks approximates the distribution of the sample mean J? for samples of size n = 5. [3] Column 3 [xbann iuD]: sample means of LUBE: samples of size n=i DD generated from an exponential distribution with mean it]. A histogram of this column approximates the distribution of the sample mean Fwith sample size n = l. a) Find the sample mean and sample standard deviation for each column (called the empirical results) and complete the following table. Please note that the standard deviation of an exponential distribution is the same as the mean. (6 marks) Mean Standard Deviation Variable Theoretical Empirical Theoretical Empirical Shape X (population) LL = X with n = 5 OF = Right skewed X with n = 100 HX = OX = Roughly Vn normal b) Draw a histogram for each column, and comment on the centre, spread (variation), and shape of the distributions. (6 marks)Summary (Dataset) xbar . n5 xbar . n100 Min. : 0. 00385 Min. : 0 . 8541 Min. : 7. 128 1st Qu. : 2. 80593 1st Qu. : 6.8861 1st Qu. : 9.255 Median : 7.08246 Median : 9.5208 Median : 9.892 Mean : 10 . 03525 Mean : 10. 1731 Mean : 9.973 3rd Qu. : 14. 05053 3rd Qu. : 12 . 7044 3rd Qu. : 10.601 Max. : 55 . 61352 Max. : 28. 1061 Max. : 13. 122