Using the normal Distribution
Suppose that the demand for a companyâ€™s product in weeks 1, 2, and 3 are each normally distributed and the mean demand during each of these three weeks is 50, 45, and 65, respectively. Suppose the standard deviation of the demand during each of these three weeks is known to be 10, 5, and 15, respectively. It turns out that if we can assume that these three demands are probabilistically independent then the total demand for the three week period is also normally distributed. And, the mean demand for the entire three week period is the sum of the individual means. Likewise, the variance of the demand for the entire three week period is the sum of the individual weekly variances. But be careful! The standard deviation of the demand for the entire 3 week period is not the sum of the individual standard deviations. Square roots donâ€™t work that way!
Now, suppose that the company currently has 180 units in stock, and it will not be receiving any further shipments from its supplier for at least 3 weeks. What is the probability that the company will run out of units?
Please keep in mind that my evaluation of your post will be based on the extent to which you participated and fostered a positive and effective learning environment–for yourself and others. Participating and sharing are the keys. Naturally, simply copying another person’s post is prohibited.
To make a post to this week’s Discussion Forum, click on the Using the Normal Distribution link, then click Start a New Conversation. In the title block of the dialog box that appears insert your first and last name; compose your post in the message box; and then click Post Message.
Your initial post(6 points) should reflect your understanding of the question posed. In addition to the computations you employed to arrive at your response, your post must contain comments regarding the rationale for the approach you utilized. Simply listing an answer is of no real value in promoting a discussion.. You must also respond to at least 2 other students. Responses(2 points each) should be a minimum of 50 words and may include direct questions.