The nation of Waipo has recently created an economic development plan that includes expanded exports and imports. It has completed a series of extensive studies of the world economy and Waipo's economic capability, following Waipo's extensive 10-year educational-enhancement program. The resulting model indicates that in the next year exports will be normally distributed with a mean of 100 and a variance of 900 (in billions of Waipo yuan). In addition, imports are expected to be normally distributed with a mean of 105 and a variance of 625 in the same units. The correlation between exports and imports is expected to be +0.70. Define the trade balance as exports minus imports.
a. Determine the mean and variance of the trade balance (exports minus imports) if the model parameters given above are true.
b. What is the probability that the trade balance will be positive?