Duration of the inspection operation in your manufacturing process is normally distributed with a mean of 𝜇=12 minutes

INSTRUCTIONS TO CANDIDATES

ANSWER ALL QUESTIONS

1. Duration of the inspection operation in your manufacturing process is normally distributed with a mean of 𝜇=12 minutes and a standard deviation of 4 minutes.

  1. What proportion of inspections last longer than 20 minutes? Answer to four decimal places. Use the Z-distribution table to answer. Explain how you developed the answer.

  2.What proportion of inspections last between 10 and 16 minutes? Answer to four decimal places. Use Minitab to answer.  Note: To answer this question, useGraph/Probability distribution plot" menu. It allows you to specify the shaded area of interest which in this case is between 10 and 16 minutes.

2. Central Limit Theorem exercise:

o In Minitab, create 10 columns called Col1, Col2, Col3,… to Col10. Name an 11th column SampleMean.

o Using the Calc>Random Data menu in Minitab, create 1,000 rows of random data points from an exponential distribution in columns 1-10. Choose your own “Scale” parameter (the same for all 10 columns) for that distribution instead of the default value of 1.0 you’ll see in the dialog box.

o Using the Calculator (on Calc menu), put the equation: (‘Col1’ + ‘Col2’ +….’Col10’ )/ 10 into the Column named SampleMean. To create the formula in the “Expression” textbox it is better to use the function keys on the calculator and add the column names by double-clicking on them in the “Select” textbox. This way Minitab will enter the information correctly. Typing by hand can lead to errors.

o  Create histograms for columns 1, 2 and 11. Column 11 (SampleMean) is a sampling distribution of the 10 columns of Exponential data. What do you notice about it?

o  Include all Minitab output and graphs in the Report. Make observations about the data in each column based on the Minitab results.

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