Problem 3 (30 Points) In the production of kraft pulp, the yield (tons of pulp per ton of wood) measured by the Kappa number, is an important control variable. A mill carries out 31 yield measurements on one of its batch digesters: 53.3 45.4 48.2 47.5 50.0 48.9 52.2 51.9 45.0 50.5 46.9 52.1 46.2 47.3 41.2 46.5 50.5 52.6 47.4 44.7 52.2 46.4 48.3 48.2 46.0 49.9 44.9 46.1 45.6 51.4 46.1 You may assume that yield measurements are normally distributed. Compute a 95% confidence interval for the true mean and the true variance. Plot the distribution for individual observations at both the lower and upper confidence limits of both the mean and variance. Use a range of yield from 35% to 61%. Under the worst case scenario, what is the percentage of batches having a yield below 45%? Identify this on the graph. How could you reduce this percentage