Zheng Xue is a diver, and she just performed a dive in an aquatics competition. There were six judges and the scores given by the judges are as follows - Judge 1 - 7.6 Judge 2- 8.2 Judge 3 - 9.2 Judge 4 - 5.8 Judge 5- 6.9 Judge 6- 8.0

Generally, 4 of the 6 scores are selected randomly and added up to calculate the final score. a. Calculate the population mean. [1 Mark] b. How many different samples of four scores are possible? [2 Marks] c. List all possible samples of size 4 and compute the mean of each. [3 Marks] d. Based on your findings what is the highest and lowest possible final scores? [1 Mark] e. Compute the mean of the sample means and compare it to the population mean. [1 Mark]