STAT 251 Lab Session #5 The Central Limit Theorem and Sampling Distribution Models The purpose of this fifth lab is to explore sampling distributions models and to use a Java applet to demonstrate the Central Limit Theorem in an interactive, dynamic way. Procedure Read and complete the following exercises. Submit the assignment to Blackboard by Monday, November 1st. Exercise 1: The Effect of Averaging Let X be a random variable representing the outcome of rolling a fair 6-sided die. The random variable can take on the values x = 1, 2, 3, 4, 5, 6 with probability 1/6 for each value. (a) Find the expected value u = E[X], the mean of the probability distribution for X. Find the standard deviation o of the probability distribution. We will use a Java applet to explore aspects of the sampling distribution for the average of n dice rolls. In particular, you will use the applet to demonstrate the Central Limit Theorem in an inter- active, dynamic way. The applet is available at the following URL: http://www. randomservices org/random/apps/DiceExperiment . html Dice Experiment | Stop: 10 . " Show Distribution Fair " Y: sum of scores Data The experiment consists of rolling n dice (1