a. What is the probability that a filled bag will weigh less than 49.5 kilograms

Learning Goal: I’m working on a data analytics discussion question and need an explanation and answer to help me learn.

Please refer to Practice problem set 3 solutions to get some guidance on this Homework and follow the structure for your solution process.

The set of problems below are Normal distribution problems.Please solve these problems using Minitab as the analysis tool and integrate your results from Minitab into your solution for each problem (You can use the “cut & paste” feature of Minitab. (Please place the results in-line with your answer to each question, not in an appendix). Make sure you structure your answers as per in-class and practice problems solutions.For each problem (and sub-problem) present the results in a short non-statistical report.(For all Normal distribution problems, it is better to draw a picture and mark all relevant information on the picture first.This will help solving the problem right)

Please do the analysis using Minitab and follow the following general structure for presenting your solution to each of the business problems:

• State the business problem in plain English
• State the equivalent statistical problem that addresses the stated business problem
• Identify and list all the necessary variables needed to address the stated statistical problem
• List all the data available to address the statistical problem
• Present the Minitab results
• State the statistical conclusions (drawn from the Minitab analysis)
• State your business conclusions/recommendations in a short paragraph or memo in plain English
• 1. A certain component for the newly developed electronic diesel engine is considered to be defective if its diameter is less than 8 mm or greater than 10.5 mm.The distributions of the diameters of these parts is known to be normal with a mean of 9.0 mm and a standard deviation of 1.5 mm.If a component is randomly selected, what is the probability that it will be defective? (Source: Unknown – 366HM?)
• 2. A farmer believes that the yields of his tomato plants have a normal distribution with an average yield of 10 lbs. and a standard deviation of 2 lbs.The farmer would like to identify the plants which yield the highest 5% and save them for breeding purposes.Calculate the yield which separates the highest 5% of yields from the lowest 95% of yields. (Source: Unknown – 368HM?)
• 3. The number of hours before a battery must be replaced in Wellbuilt watches is normally distributed with a mean of 1,900 hours and a standard deviation of 145 hours.What proportion of watch batteries fail before 1,600 hours?Suppose that during the next six months, more than 50% fail before 1,600 hours.From a problem-sensing perspective, what might you conclude?Explain (Source: Unknown – 290BS?)
• 4. Canine Crunchies Inc. (CCI) sells large bags of dog food to warehouse clubs.CCI uses an automatic filling process to fill bags.The weights of the filed bags are approximately normally distributed with a mean of 50 kilograms and a standard deviation of 1.25 kilograms

a. What is the probability that a filled bag will weigh less than 49.5 kilograms

b. What is the probability that a randomly sampled filled bag will weigh between 48.5 and 51 kilograms

c. What is the minimum weight a bag of dog food could be and remain in the top 15% (by weight) of all the bags filled?

(Source: GSFS-Eighth edition)

5. An Internet retailer stocks a popular electronic toy at a central warehouse that supplies the eastern United States. Every week the retailer makes a decision about how many units of the toy to stock. Suppose that the weekly demand for the toy is approximately normally distributed with a mean of 2,500 units and a standard deviation of 300 units.

a. If the retailer wants to limit the probability of being out of stock of the electronic toy to no more than 2.5% in a week, how many units should the central warehouse stock?

b. If the retailer has 2,750 units on hand at the start of the week, what is the probability that weekly demand will be greater than inventory?

c. If the standard deviation of weekly demand for the toy increases from 300 units to 500 units, how many more toys would have to be stocked to ensure that the probability of weekly demand exceeding inventory is no more than 2.5%? (Source: GSFS-Eighth edition)

Questions?

If something is not clear, ask for clarification by emailing me (I am available to help you learn).Do not answer the wrong question (and commit a type III error) and get penalized on the grade.

Hints:

Here are some common mistakes made on this HW & some suggestions to avoid them: