Question $13$

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An important aspect of customer service and satisfaction at the Big Country theme park is the maintenance of the washrooms throughout the park. Customers expect the washrooms to be clean; odorless; well$-$stocked with soap; paper towels, and toilet paper; and to have a comfortable temperature. To maintain quality, park quality$-$control inspectors randomly inspect washrooms daily $($during the day and evening$)$ and record the number of defects $($incidences of poor maintenance$).$ The goal of park management is approximately $10$ defects per inspection period. The Excel workbook posted to Moodle contains a summary of the observations taken by these inspectors for $20$ consecutive inspection periods.

Construct the appropriate control chart for this maintenance process using $30$ limits$.$

$\backslash$table$[[$Sample Number of Defects,$],[1,7],[2,14],[3,6],[4,9],[5,12],[6,3],[7,11],[8,7],[9,7],[10,8],[11,14],[12,10],[13,11],[14,12],[15,9],[16,13],[17,7],[18,15],[19,11],[20,16]]$

What is the $30$ upper control limit for this data? $($Round to $2$ decimal places.?

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