Reference no: EM131176034

Requirement :

As the communication mechanism of the analysis process, the memo should provide a coherent synopsis of the problem, identify different options for addressing the problem, articulate opposing perspectives, and advocate for a recommended option. The typical structure for a memo includes: a description of the objective; relevant background information; a discussion of key considerations (including implementation concerns, financial considerations, stakeholder impacts, and possible unanticipated consequences), a summary of arguments for and against, and a recommended decision.

Q1:: Organizing and Interpreting Data Scenario Assignment

Scenario Script

Caption Text: After several productive years, Princess Foods Corporation has amassed enough capital, marketing identity, and operational expertise to make a major push into new product lines and markets. To help manage this growth, Princess Foods Corporation has hired you as a consultant.

Princess Foods Corporation has been considering a new offering, a premium, high-quality ice cream that is low in sugar and calories. This new "Tiara" line will be offered to customers in exotic flavors, such as Avocado Sea Salt, Ginger Rosewater, and Rosemary Goat Milk, and will use locally sourced, organic ingredients.

Bonnie: Well, I suppose we might as well just throw you into the fire. We've been piloting the "Tiara" line for the past 50 weeks. I have a presentation to the board on Tuesday and they're going to be expecting an update on the pilot. Could you wade through this data and put together a short report for me? I'm glad you're here.

Here's the raw data. Can you organize this?

Assignment
Bonnie has an upcoming presentation to the board and would like to include some market research from the pilot period.

Below are the profits and losses in thousands for Princess Foods Corporation for 50 weeks. The data reflects the performance of the "Tiara" line during the period of the pilot.

Provide Bonnie with the following data in a short report:

1. Determine the number of classes, the class range, and then construct a frequency table.

2. Interpret information from the frequency table.

3. Calculate the most appropriate measure and central tendency and explain why that measure was selected.

4. Determine the percentile indicating the top highest ranking 30%

Q2: Empirical Rule as it Relates to Normal Distribution Scenario Assignment

Scenario Script

Caption: Production at the Burlington facility of the Princess Foods Corporation has been found to occur at a normal distribution. While some weeks are extremely productive and others fall far enough below the average to be considered especially unproductive, production generally follows the pattern of a bell curve.

Bonnie: I'm still concerned that the quality control issues will cause production to drop too low. We have another board meeting in a few weeks. If production dips that week, we are in bad shape.

Caption: Depending on the timing, an off week could have an inordinately large impact on the business if that bad week is enough to make shareholders skittish.

Bonnie: Can you to do some research on the probability that production will stay above targets on any given week?

Assignment
Use the empirical rule to draw conclusions about the data set below and to determine the probability of Modules produced per week at Princess Foods Corporation.

Production has been determined to be a normal distribution
Average production is 5,000 Modules per week with a standard deviation of 200

Answer the following questions:
1. What is the probability that next week's production is between 4,800 and 5,400?

2. What is the probability that next week's production be less than 4,400?

3. What is the probability that next week's production is between 5,200 and 5,600?

Q3: Random Variable Distributions Scenario Assignment

Scenario Script

Caption: Princess Foods Corporation purchases glass containers from China for the packaging of their high- end soups. These shipments come to Princess Foods Corporation in skids that were transported across the Pacific Ocean in giant shipping containers. When glass jars are shipped internationally, a small degree of defects is inevitable.

Liwei has negotiated a deal with the vendor that an overall defect rate of 5% is acceptable. If more than 5% of the jars on a given skid are defective, Princess Foods Corporation does not have to pay for that shipment. If the defects are greater than 5%, that shipment is returned (at the shipper's expense).

Liwei: There's a possibility of an increase in demand and therefore production. Will we need more glass jars?

Bonnie: Can you take a look? I've noticed that the work that you're doing here seems to take the guess work out of things and...I really respect that. I'd love to hear your thoughts.

Assignment
If 20 samples of product are randomly selected and tested, what is the probability of the following:
1. Exactly two samples are defective

2. Between two and five inclusive are defective

3. Less than four are defective

Q4: Normal Distribution Using the Z Formula Scenario Assignment

Scenario Script:
Caption: Princes Foods Corporation is going through their annual labor negotiation with their unionized employees. Bonnie and Liwei are doing their due diligence and would like to know how a strike at Princess Foods Corporation would negatively affect the number of cans of creamed peas produced per day if the workforce is not at full capacity.

Bonnie: Let's think through the worst-case scenario: there's a strike and we don't have our normal workforce. What do we do?

Liwei: Before or after I have a heart attack?

Bonnie: Ha! Let's say you have a heart attack on Friday and recuperate over the weekend. You come into work on Monday and we've shifted to our contingency plan.

Liwei: Okay, right. We would have management and other non-unionized employees in place to operate the machinery.

Caption: Use the data below and apply the principles of normal distribution using the z formula in order to determine the probability of units produced per day at Princess Foods Corporation.

Assignment
The average number of cans of creamed peas produced each day at the processing plant is 20,000 with a standard deviation of 2,300. Assuming a normal distribution, answer the following questions:

1. What is the probability of producing more than 26,000 cans per day?

2. What is the probability of producing between 18,000 and 23,000 cans per day?

3. What is the probability of producing between 22,000 and 24,000 cans per day?

Q5: Calculating X from a Known Probability Scenario Assignment

Scenario Script:
Caption: The possibility of a labor stoppage at Princess Foods is becoming greater and greater as the collective bargaining negotiations with the union have broken down.

Although they have a contingency plan for management to operate the machinery if a strike should occur, they only have enough people trained to cover 5% capacity of the normal distribution.

Bonnie: I am getting more and more uneasy about this situation. We've had four formal complaints filed already.

Liwei: Even with our contingency plan in place, we need more concrete information about how a labor stoppage could affect production numbers. I know that you've helped us with this already, but could you take another look? Exactly how many cans could be produced per day under these circumstances?

Assignment
The average number of cans of creamed peas produced each day at the processing plant is 20,000 with a standard deviation of 2,300.
How many cans would be produced per day under these circumstances?

Q6:M2d: Bayes Theorem

Scenario Script
Caption: Bonnie needs you to investigate some quality control issues at the Burlington factory.

Bonnie: Thanks for coming in. We're working through a problem at our Burlington factory. During a recent spot check of our Fruit Cocktail inventory, the number of defects that we found exceeded our quality standards. That means we had to throw out a good bit of inventory.

Liwei: I am not a happy man. Throwing out inventory is like throwing away money.

Bonnie: Well, that's why we have quality assurance. The way I look at it, we've got an opportunity to improve our quality. Tell me about the Burlington factory. There's a new training initiative that I'd like to test, that could improve our manufacturing processes...

Liwei: Our work force at the Burlington factory is divided into two shifts; a morning shift and a night shift.

Bonnie: Do we know which one would benefit the most from training?

Caption: The Burlington plant uses two separate work shifts, morning shift (6:00 am to 2:30 pm) and night shift (5:00 pm to 1:30 am). The morning shift produces 65% of the product, while the night shift produces the remainder.

Assignment
The Quality Control department indicated that given the product was produced in the morning shift, there was a 5% defective rate. While given the product was produced during the night shift, there was an 8% defective rate. The Bayes Theorem will help you determine the probability that these defects are an indicator of an underlying quality control issue. Construct a contingency table using the information provided or use the Bayes formula to answer the questions below and interpret your findings and suggest recommendations. In your response, make sure that you explain and justify your answers:

1. Given the finished product is defective, what is the probability it was produced during the day shift?

2. Given that the product is defective, what is the probability the finished product was produced during the night shift?
Princess Foods has the budget to provide one shift with additional training that should mitigate quality control issues. Should one shift undergo additional training?

Q7:Sampling and Confidence Intervals

Scenario Script
Caption: Mieke, the head of Marketing has heard about you. And at Princess Foods, like much of the rest of the world, the reward for good work is more work.

Mieke: Thank you so much for making time for me. Liwei says that you're a miracle worker...

Caption: Princess Foods Corporation is piloting a new service called "Princess Select," a new premium meal kit service. Subscribers are mailed kits that each contain all the ingredients that a customer would need to make a delicious meal in exactly the right proportions. All the customer needs to do is to follow the provided recipe and a fresh, home-cooked meal is ready in no time. Mieke needs to gauge their interest in this new service and decide whether to market it nationally.

Caption: Mieke has stated that at least 85% of the potential customers must express some desire for the service and, for those who exhibit an interest, the average cost they are willing to pay per two-meal package must be at least $47.50. Mieke insists that you be 95% certain of your findings.

Mieke: Because this is a relatively new service on the market, we need some additional insight into how Princess Select would fit into our customers' lives and what they'd be willing to pay for a service like this. We conducted a survey of 50 potential customers. Can you prepare a memo that includes your findings and recommendations?

Assignment
In your memo, you should include the raw data and a clear interpretation of the data that justifies your findings. Use the raw data below to write your memo. Since you only have sample data, you decide to determine confidence intervals.

Of the 50 potential consumers surveyed, 34 expressed an interest in purchasing it. The maximum price each would be willing to pay is shown in the table below.

Using the data, answer the following questions:
1. How would you reply to the Mieke's request for information?

2. Should the service be marketed?

3. How large should the sample be if you want to maintain a 95% level of confidence and suffer a maximum error of $2.00 in your estimate of the highest price consumers are willing to pay?