= 4. a). [5 points] Sketch the function x4 = x + 0.1 between x = - 2 and + 2 and find the positive root to 4S accuracy using the Newton-Raphson method. Choose your Xo wisely for minimum iterations and show your work! b). [3 points] Assuming the lifetime of your product is normally distributed with a mean of 3 years and a standard deviation of 1 year, what percentage of your products would you have to replace if you guarantee your products for 2 years? If the standard deviation were smaller, would the percentage be smaller or larger? Why? c). [12 points] Five samples of size two for the thickness X of washers were recorded as (2.74, 2.76), (2.74, 2.74), (2.79, 2.81), (2.78, 2.76), (2.71, 2.75). Determine the mean (u) and variance (o) and set up a control chart for the mean. Also find the lower and upper control charts for the variance and standard deviation for a = 10%