Suppose that you wanted a 95% confidence interval for the mean of a normally distributed random variable whose actual mean is 10 and whose actual standard deviation is 5. Using the method described in class, calculate the sample size m necessary for the 95% confidence interval to have a width of 3 units. Please use the following procedure and report your results at each step. Since we specify a 95% confidence interval, the value of c that you will use is c = 2. (In case you are curious, the precise value of c for a 95% confidence interval is c = 1.96, which is a number you may recognize from a previous statistics course. For our purposes, 2 is close enough.) Generate 15 random numbers from a normal distribution with mean 10 and standard deviation 5. You can do this using the same Excel syntax that you used for POD #7 (just changing the mean and standard deviation). Calculate the sample standard deviation of the 15 values. Make sure that you use the Excel command = STDEV.S for this step. Use this sample standard deviation to calculate the number of Monte Carlo values necessary to achieve a 95% confidence interval for the mean, with the desired width of less than 3 units. If your value of m is not an integer, round up to the next integer. For example, if you calculate m = 35.03, you would round up to m = 36. Generate this number of random values from the normal distribution and report the average value and the confidence interval for the mean. Be sure to show the details of your confidence interval calculation. Is the actual mean of the normal distribution (10) within the confidence interval? Is the width of your confidence interval within the desired band (w* = 3)?