Reference no: EM132013372

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?

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