The monthly sales demand for a new product is uncertain, but it is considered to be adequately described by a normal random variable with mean 50,000 units and variance 100,000,000.

(a) A factory to manufacture the new product has been constructed with enough capacity to meet sales demand 90% of the months. How much capacity does the factory have?

(b) The accounting department has indicated that there is a 27% chance that the new product will not generate enough monthly sales volume to make a profit. What is the break-even sales level per month?

(c) Find an interval for the observed monthly sales, which is symmetric around the mean of the monthly sales, such that next month's sales have a 0.9 probability of being within the interval.