5.99 Big Nail Construction Inc. is building a large, new student center for a famous Midwestern liberal arts college. During the project Christine Buildumbig, the project manager, requests that a pile of sand weighing between 138,000 pounds and 141,000 pounds be placed on the newly constructed driveway.

You have been asked to determine the probability that the delivered sand satisfies Christine’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 80,000 and a variance of 1,000,000, and sand loads in the small truck are also normally distributed with a mean weight of 60,000 pounds and a variance of 810,000. From past experience with the sand-loading facility, you know that the weight of sand in the two trucks has a correlation of 0.40. What is the probability that the resulting pile of sand has a weight that is between 138,000 and 141,000 pounds?