##### Binomial Distributions

Given your statistical knowledge, you have been asked to assist the quality control manager of a local manufacturer in establishing and seeing that the factory conforms to standards set by management. The facility manufactures a new electronic toy.

The factory can produce 1000 toys per day. Management has indicated that initially they will be satisfied if the defect rate is 3% or less.

Since you can’t quality-test every toy produced, you suggest that a random sample of 40 toys be taken. The results of testing 40 toys from today’s production line yields the results shown in the “WA3_Outcomes” Excel file Column 1.

Using Excel and this data:

- Create a pivot table.
- Analyze the result.
- Provide rationale relative to management’s target being met, your sample size of 40, and how representative the sample might be to the population.

Take a second sample of 40 toys. The results of this sample are shown in “WA3_Outcomes” Excel file Column 2.

- Create a pivot table for this sample.
- Analyze the result.
- Provide a rationale for how the knowledge gained from taking a second sample changes or does not change your analysis.

Since there are just two outcomes from the test, defective/not defective, you decide to utilize your knowledge of binomial probability distributions to assist the quality control manager in preparing a report for management.

- Using the Excel binomial distribution function, create a sampling distribution of the number of defects in each of many, many samples with the sample size of 40 and the target percent defective in the population equal to 3%.
- Analyze the result.
- Provide rationale relative to management’s target and your initial sample size of 40.
- Create a sampling distribution of the number of defects in each of many, many samples with the sample size of 200, but with the percent of defective toys you calculated in the second pivot table.
- Provide rationale relative to management’s target and your initial sample size of 40.
- How has the increase in the sample size changed your analysis?