Since the key to profitability was the difference between these two random variables, a third derived random variable d = x - y was used to determine the probability distribution for x and y. In turn, this information was used to develop a continuous probability distribution for the difference d. Using the continuous probability distribution, it was observed that there was a.90 probability that the price difference would be $.0655 or less. and that there was a.50 probability that the price difference would be $.035 or less. In addition, there was only a.10 probability that the price difference would be $.0045 or less.
The Industrial Chemicals Division thought that being able to quantify the impact of raw material differences was key to reaching a consensus. The numbers obtained were used in sensitivity analysis of the raw material price difference. The analysis yielded sufficient insight to form the basis for a recommendation to management.
The use of random variables and continuous probability distributions was helpful to P&G in analyzing the economic risks associated with it's fatty-alcohol production. In this chapter,you will gain an understanding of continuous random variables and their probability distributions including one of the most important probability distributions in statistics, the normal distribution.