5.99 PowerChina, a Chinese construction company, is building a large, new retail center at the Chengdu Industrial Development Zone, Sichuan. Yao Minhao, one of the project managers, requests that a pile of sand weighing between 140,000 and 142,000 pounds be placed on the newly constructed driveway. You have been asked to determine the probability that the delivered sand satisfies Yao Minhao’s request. You have ordered that one big truck and one small truck be used to deliver the sand. Sand loads in the big truck are normally distributed with a mean of 90,000 and a variance of 1,200,000, and sand loads in the small truck are also normally distributed with a mean weight of 50,000 pounds and a variance of 600,000. From past experience with the sand-loading facility, you know that the weight of sand in the two trucks has a correlation of 0.20. What is the probability that the resulting pile of sand has a weight that is between 140,000 and 142,000 pounds?

5.100 An investment portfolio in Finland specializes in pulp and paper stocks and includes two of them. One is Valmet (mean 0.1; standard deviation .025), and it accounts for 40% of the portfolio shares. The other Finnish pulp and paper manufacturer present in the portfolio is Stora Enso (mean 0.22; standard deviation 0.3), a higher-risk, higher-return investment.

a. What is the expected value and the standard deviation of the portfolio if the coefficient of correlation of the two stocks is 0.7?

b. What will they be if the correlation is 0.4 instead?