Delta Sonic is a car wash provider in Western New York. VIP Customers at their Buffalo,...

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Delta Sonic is a car wash provider in Western New York. VIPCustomers at their Buffalo, NY location sign up for unlimited carwashes and a separate line & dedicated car wash services thosecustomers (i.e. a single-server single-queue model). Assume VIPcustomers arrive every 10 minutes on average and that theirinter-arrival time is exponentially distributed. Also, assume thatprocessing (washing) time is the sum of two components:
A constant (i.e. not random) basic washing time that isexactly 4 minutes.
A random extra-service time that is exponentially distributedwith mean time of 2 minutes.
In Excel, simulate the arrival times and processing times of VIPcustomers at this car wash using 2,000 sample customers. Using theresults of your simulation, calculate the percentage of VIPcustomers that were in the process (i.e. waiting+washing) forlonger than 12 minutes. Press F9 to rerun your simulationseveral times and record the results for the percentage ofcustomers who wait longer than 12 minutes. Using the median ofthese recorded percentages as your estimate of the percentage ofcustomers expected to wait longer than 12 minutes, enter thatprobability here as a two digit decimal e.g. 0.25, 0.45, 0.99,etc.)

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AnswerFirst I have Prepared Simulation data for 2000 Sample withConstant Arrival time Constant Wash Time and Random Extra ServiceTimeRandom Extra Service Time Calculation In MS ExcelNORMINVRANDI1I2I1 Mean value given 2 MinutesI2 Standard Deviation Value 15 Minutes Considered forGenerating Random Number1st Random number generated in one cell then dragged to allcell total 2000 cellLets do Normality test for the Total Time include Arrival TimePlus Constant Wash Time and Extra Service Time then for totaltime as P Probability value is more than 005 therefore Totaltime data is normally distributedNormality Check for Total Time Data in MiniTab 2017 Stat basic Statistics Normality Test select Variable Total Time Anderson darling Normality Test will come below likeNow Calculated Mean Time and Standard deviation for Total Timedata where In MiniTab 2017 Path StatBasicStatisticsDisplay Descriptive StatisticsI will get result likeMean Time for Total Time data 15994Standard deviation for Total Time data 1522Now In Minitab 2017 Go to Graph Tool Bar ProbabilityDistribution PlotView ProbabilityDistribution Normal asTotal time is Normally Distributed Select Mean 15994 Standarddeviation 1522 Keeping X Value Right Tail 12 will get Resultlike belowSo The percentage of VIP customers that were in theprocess ie waitingwashing for longer than 12 minutes is 09957X 100 9957 and The Probability is 99Simulation data of 2000 Sample in MS Excel format herecant be uploaded so only 500 samples data presented for reference which used for above calculationSl NoArrival TimeMinutesConstant Wash timeExtra See Answer

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