# Business Statistics and Quantitative Analysis - Checking for Quality

*label*Mathematics

*timer*Asked: Dec 19th, 2018

*account_balance_wallet*$35

**Question description**

Scenario: A venture capitalist has just given you several million dollars to develop your dream product! Explain in detail what this product is and why people would buy it. (Think Steve Jobs and the iPhone - did people really think we needed “smartphones” back in 2007?)

Main Post: Now your dream product has gone into production and the manager is asking you, as the statistical expert, to use statistical methods to ensure quality control.

1. You will generate a random dataset of N samples of defective proportions by completing the following steps:

a) You will start with a random number by combining the last 2 digits of the year in which you were born plus the day of the month in which you were born. For example, if you were born October 3, 1990, your number would be 90 + 3 = 93. (If your number exceeds 100, subtract 100 from the total.) Call this X and it will seed your random number generation. MY DATE OF BIRTH IS 9/4/1978.

b) Choose a number of samples, N. (N should be between 5 and 10 samples.)

c) In Excel, type =RAND()*X in a cell. Repeat N times. This will generate the proportion of defective products (out of 100) for your N samples.

2. Use Excel to create a p-chart for a sample size, 100, and the number of samples, N.

3. Write a professional memo to your business/company owner describing the production quality so far and prioritizing any control measures necessary to guarantee high quality products.

Address the following items and questions in your professional memo:

- Describe your product, its use, and societal value. (Humor is encouraged.)
- Share and summarize your p-chart.
- What is your Lower Control Limit (LCL) and Upper Control Limit (UCL)?
- Is the product in control? If not in control, what sample(s) was outside of the limits, i.e., below LCL or above UCL?
- What measures could be taken now to address the data points that out of control?
- What recommendations would you suggest to optimize quality in future production?

## Tutor Answer

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