# Topic: Using the Normal Distribution

*label*Mathematics

*timer*Asked: Jan 21st, 2019

*account_balance_wallet*$10

### Question Description

Hi!

here is another one, willing to help?

Forum:

Suppose that the demand for a company’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 don’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?

Instructions:

Excel, is going to be your best friend for some of these calculations. Check out the function normdist in Excel! You can use this instead of table E in our book. The full description tells you how to calculate the mean and variance, but not the standard deviation. As a hint, use your calculated variance to find the standard deviation.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. Your initial post 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.

## Tutor Answer

See attached

Normal Distribution

The first step is to find the mean and standard deviation for a three week period. The mean for a

three week period will be the sum of the weekly individual means

Mean = 50+45 +65 = 160

The variance for a three week period will be the sum...

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