Suppose that items from a manufacturing process are subject to three separate evaluations, and that the results of the first evaluation X1 have a mean value of 59 with a standard deviation of 10, the results of the second evaluation X2 have a mean value of 67 with a standard deviation of 13, and the results of the third evaluation Xx have a mean value of 72 with a standard deviation of 4. In addition, suppose that the results of the three evaluations can be taken to be independent of each other.
(a) If a final evaluation score is obtained as the average of the three evaluations X = (X1 + X2 + X3)/3, what are the mean and the standard deviation of the final evaluation score?
(b) If a final evaluation score is obtained as the weighted average of the three evaluations X = 0.4X1 + 0.4X2 + 0.2X3, what are the mean and the standard deviation of the final evaluation score?