1. 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.
1. From past experience, an auditor knows that the dollar value of the accounts receivable for the ABC Corporation, denoted by the random variable X, has a normal distribution. Unfortunately,
she has forgotten the mean and variance of the accounts receivable distribution. One of her staff members has informed her that the following probability statements are true: P(X ≤ 5000) = 0.25 and P(X ≥ 7000) = 0.25.
(a) What are the expected value and variance of X?
(b) What is the probability that one account drawn at random will have a dollar value equal to 8500?
(c) What is the probability that one account drawn at random will have a dollar value between 5500 and 5800?