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Operations and production managers often use the normal distribution as a probability model to forecast demand in order to determine inventory levels, manage the supply chain, control production and service processes, and perform quality assurance checks on products and services. The information gained from such statistical analyses help managers optimize resource allocation and reduce process time, which in turn often improves profit margins and customer satisfaction.

Based on your understanding of the characteristics of the normal distribution, examine the chart below. Process A standard deviation is .9, Process B standard deviation is 1.4, and the mean of both processes is 12.

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1. Do either of the processes fit a normal distribution? Why or why not?

Yes: The second graph is close to a normal distribution, generally as we increase sample sizes from 1 we will see the graphs approach normal distribution and at around n=30 the two start producing similar values

2. Which of the processes shows more variation? What does this mean practically?

By observing the two processes B curve is more spread out than A indicating that Process B values has high variation. Practically this means that we expect process B to produce values which are more distant from mean as compared to A. A can be said to be more consistent than B

3. If the product specification quality limits were 12 +/- 3, which of the processes more consistently meets specification? Explain why.

Specification Limits 12 +/- 3 mean that if the process is producing values below 9 and above 15 will be considered to be out of control; from the above graph process A is seen to produce values which are in this range while B has values outside this range. Therefore A will be consistent than B , B will run of out of control severally

4. If the product specification quality limits were changed to 12 +/- 6, is quality loosening or tightening? Which process would benefit the most from this change?

This change makes quality to loosen because we are ready to accept goods whose quality is far much from the average quality (mean) so the process will sometimes produce goods which are of poor quality sometimes which are of high quality without crossing the limits in other words we are accepting extreme defectives than the first time

5.Are there processes at your place of employ that you believe follow a normal distribution? If so, describe one. Why do you believe it is normal?

Yes: in filling of bottles, a normal distribution based process is used to control the amount of water filled in each bottle to ensure that it conforms to the specifications, if the filling machine is wearing out the process starts to run out of control and overfill or under fill the bottles. The normal distribution is trusted because it depends on sample size which is something we can control.

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