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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
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%?
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.
Here are some common mistakes made on this HW & some suggestions to avoid them:
Not specifying your answer clearly (and require the instructor to fish for the answer)
Explicitly follow the seven parts (a through g) structure to answer each question. Also, follow the structure in in-class and practice problem set solutions for your answers.
Not addressing all the requirements
Read and follow all instructions.Create a checklist for your use to insure your report meets/addresses all requirements.
Not including a graph for each problem part
Include Minitab graphs
Not separately stating your answer
State the answer to each part in mathematical terms and with a business conclusion, Follow the in-class and practice sets as examples.
Stating the answer/probability for the wrong end of the curve
It is easy to mix up the ends of graphs and have an answer that is “1 minus the correct answer.” At the end when you state your answer, make sure it makes logical sense. For example, if the mean on the test is 85 and you are asked for the score of the top 5%, an answer could be 95 – an answer of 75 (the bottom 5%) would not make sense.
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