The company you work for, MBF Nutrition, makes a specialized supplement for older dogs that is added to their food. One of the company's products is a 100-gram bag of high-protein dog food. The bags are filled by a single machine that is very accurate in the long run with respect to the mean fill weight. However, this machine also has high variance, resulting in a higher-than-desired number of bags that are underfilled or overfilled.

A bag is considered underfilled if it weighs less than 99.4 grams and overfilled if it weighs more than 100.8 grams. James Cary, your supervisor, has provided you with 12 days of data about the number of underfilled and overfilled bags. The company produces 1,000 bags each day. The data is as follows: 95, 100, 82, 84, 84, 69, 92, 100, 81, 86, 87, 66.

Each bag that is overfilled or underfilled costs the company an estimated $2 in lost time and labor. Jim has asked you to prepare a one-page Word document memo that includes:

1. The upper and lower bounds of a 95% confidence interval for the mean number of overfilled and underfilled bags.
2. Estimates of the yearly low and high costs, using the upper and lower bound confidence interval estimates. Consider that the interest rate is 2.5% per quarter and remember that your data is in days.

Please ensure the memo is clear, concise, and formatted professionally.

Using statistical operations, calculate the 95% confidence interval for the mean number of overfilled and underfilled bags, then estimate the annual low and high cost by incorporating the cost per bag, production days and interest rate.

Explanation:

To answer your question, we are going to use some statistics to calculate the 95% confidence interval for the mean number of overfilled and underfilled bags and then make a financial determination on the low and high cost estimates.

The data you provided looks like raw data of the number of bags that are over- or under-filled from the last 12 days. We'll first need to compute the mean (average) and the standard deviation of this data. Once we have these, we can use the t-distribution to find the bounds of the 95% confidence interval - these calculations are a common exercise in statistics.

To estimate the yearly low and high cost, we'll multiply the lower and upper bounds of the confidence interval by the estimated cost per bag, the number of production days in a year, and then also take into account the interest rate of 2.5% per quarter.

Please remember these are just estimates and actual costs could be different based on a variety of factors not considered in this simple analysis.

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