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# BA 303 - BUSINESS STATISTICS - Week 3: Learning Unit 2: Discussion 1: Chapter 5, Problem 40

BA 303 - BUSINESS STATISTICS - Week 3: Learning Unit 2: Discussion 1: Chapter 5, Problem 40

Week 3: Learning Unit 2: Discussion 1: Chapter 5, Problem 40

**A supplier contract calls for a key dimension of a part to be between 1.96 and 2.04 centimeters. The supplier has determined that the standard deviation of its process, which is normally distributed, is 0.03 centimeter. **

**If the actual mean of the process is 1.98, what fraction of parts will meet specifications?**

**If the mean is adjusted to 2.00, what fraction of parts will meet specifications?**

**How small must the standard deviation be to ensure that no more than 2% of parts are nonconforming, assuming the mean is 2.00?**

o begin this problem I created a formula that would show the data with the mean and standard deviation increments. I normalized the data and created a scatterplot so I could have a visual. To determine what fraction of parts was specified I highlighted the data that was in between the specifications of 1.96 and 2.04 centimeters. From that I was able to determine that when the mean is changed the data just widens. With part A, the specifications have the data within -.6 and 2 standard deviations. Since the problem is normal we can use z-scores to determine what percentage of the data is within the parameters. 85.145% of the parts meet the requirements.

This is the histogram created with a mean of 1.98 and a standard deviation of .03.

For part B all I had to change was the mean and the formulas did all the work. Since the problem specified that it is normal the data widens with the new mean. I attached the second histogram with the new mean to see the difference between the two charts. With the new mean, the parameter now mean the data goes to 1.3 standard deviations on each side. This means 90.32% of the parts meet the requirements.

For part C of the problem I was not sure how to apply the goal seeking tool so my answer is not as exact. First I found the z-score that I needed and converted it back into a standard deviation that would get 98%. After realizing that I do not understand how I am supposed to use the goal seeking tool to have something be between I tested by changing the standard deviation. This way I was able to see when the parameter reached 2 standard deviations. I found that with a standard deviation of .02 one can have 98% of parts be useable.

To summarize, this analysis tool could be used to find where production should be improved to have a better outcome of useable parts. I think that if I could understand how the goal seeking tool could be used in this problem I would understand a lot better because I do not know how what I am supposed to put in.

References

Evans, J. R. (2019). Chapter 5. In *Business analytics* (3rd ed.). Pearson.

CowanAcademy. (2017, December 19) *How to create a bell curve in Excel using your own data*[Video]. Youtube. https://www.youtube.com/watch?v=OcXxMk6qG6U (4:37)