Solve these problems and upload your solution to Canvas. You can solve them $"$by hand" or

using Excel.

Show all your work $($typed in the document or pasting a scanned image of your handwritten

solution$).$ Save your solution document in a $.$pdf file and upload it to Canvas along with an

Excel file for calculations performed in Excel.

Problem $1(18$ points$)$

The following is a control chart for the average number of minor errors in $22$ service reports.

a$.$ Determine the observed number of runs $($median$,$ and up$/$down$),$ expected number of runs,

standard deviation, and the z$\_("$test $")$ value for the median and up$/$down test. Use z$=+//-2$ to compare

your z test scores. $($Negative amounts, if any, should be indicated by a minus sign. Round your

answers to $2$ decimal places.$)$

Please use the table below to summarize your answer.b$.$Based on your calculations, conclude whether the test is random or non$-$random. Use the criteria of $($associated to a $95\mathrm{.}5$ confidence level$)$ to evaluate if there is non$-$random error.

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Test

Conclusion $($Random or Nonrandom$)$

Median

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Up$/$Down

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$$c$.$ Should the process be investigated due to nonrandom variation? $($Yes or No$)$

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Problem $2(4$ points$)$

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The Healthy Chocolate Company makes a variety of chocolate candies, including a $12-$ounce chocolate bar $(340$ grams$)$ and a box of six $1-$ounce chocolate bars $(170$ grams$).$

a$.$Specifications for the $12-$ounce bar are $336$ grams to $344$ grams. What is the largest standard deviation $($in grams$)$ that the machine that fills the bar molds can have and still be considered capable if the average fill is $340$ grams?$($Round your intermediate calculations to $2$ decimal places and final answer to $3$ decimal places.$)$

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Standard deviation: $\_\_\_\_\_\_\_\_\_\_\_\_\_$ grams.

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Problem $3(8$ points$)$

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As part of an insurance company$$s training program, participants learn how to conduct an analysis of clients$$ insurability. The goal is to have participants achieve a time in the range of $30$ to $45$ minutes. Test results for three participants were the following: Armand, a mean of $36$ minutes and a standard deviation of $3$ minutes; Jerry, a mean of $35$ minutes and a standard deviation of $3\mathrm{.}0$ minutes; and Melissa, a mean of $37\mathrm{.}5$ minutes and a standard deviation of $1\mathrm{.}8$ minutes.

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a$.$Compute process capability for$$the participants and determine whether each is capable.$($Do not round intermediate calculations. Round your answers to $2$ decimal places.$)$

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Participant

Cpk

Cp

Armand

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Jerry

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Melissa

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Problem $4(15$ points$)$

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Processing times for new accounts at an investing firm are provided in the file $$Ch $10$ Procedure Problems $$ P$4$ data.xlsx$..$ Twenty samples of five observations each have been taken. Use the sample data in conjunction with Table $10\mathrm{.}3$ in our textbook to construct upper and lower control limits for a mean chart. Do the results suggest that the process is in control? Why or why not? $[$Hint: Consider Solved Problem $2$ in page $456$ in our textbook as you work on this problem. I highly suggest you use Excel to solve this problem.$]$