PROBLEM 2: (20 Marks) The Manager of a local Starbucks Coffee Shopis interested in improving the service provided to customers at the coffee shop. As a first step in the process, the manager asks his assistant to record the number of arrivals between 9:00 A.M and 10:00 A.M., since this is the busiest time of the day. The number of arrivals during this time interval, for a number of days, are included in the excel file titled “StarbuckesArrivals_21”. This file is posted on Sakai in the Data Folder. Given the background and the data, answer the following questions: a) Use the “Excel” spreadsheet application to calculate the average, standard deviation, variance, maximum, minimum, and range for the observations entered in the attached excel file. Interpret these values from a business point of view. In other words, instead of saying ‘the variance of the distribution is “x.xx”‘, provide a one-sentence explanation of the value in non-technical terms, so that someone not familiar with statistical jargon can understand the meaning of the results you have obtained. (4 Marks) b) Develop a frequency chart for the data. Without performing any technical analysis, interpret if the frequency charts resemble any of the probability distributions you learned in this course. Use the Bin Values 1, 3, 6, 9, and 12. (Note: there may be data outside of this range and you are required to handle it accordably.) (5 Marks) c) Do Chi-Square goodness of fit test to determine if the data, based on the bin values in b above, is from a Poisson distribution. Use a = 0.05 for your test. (6 Marks) d) Assuming that the data does conform to Poisson distribution, what is the probability that there are exactly 3 arrivals between 9:00 A.M and 10:00 A.M.? What is the probability that there are between 2 and 6 arrivals, inclusive, between 9:00 A.M and 10:00 A.M? What is the probability that there are more than 7 arrivals between 9:00 A.M and 10:00 A.M? To solve for the probabilities, use two approaches. First, calculate the probabilities using POISSON.DIST excel function, using the sample mean as your estimate for Lambda. Then, solve the probabilities from the data. For the second method, use the observations, and the relative frequencies, which you can find using the Frequency Function with Bin Values of 0, 1, 2,…,7. (5 Marks)MathStatistics and Probability ITIS 1P91

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