Prairie Flower Cereal has annual sales revenue of $400,000,000. George Severn, a 58-year-old senior vice president, is responsible for production and sales of Nougy 93 Fruity cereal. Daily production in cases is normally distributed, with a mean of 100 and a variance of 625. Daily sales in cases are also normally distributed, with a mean of 100 and a standard deviation of 8. Sales and production have a correlation of 0.60. The selling price per case is $10. The variable production cost per case is $7. The fixed production costs per day are $250.
a. What is the probability that total revenue is greater than total costs on any day?
b. Construct a 95% acceptance interval for total sales revenue minus total costs.