The Manager of a local StarBuckes Coffee Shop is interested in improving the service provided to customers

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Question:

The Manager of a local StarBuckes Coffee Shop is interested in improving the service provided to customers at the coffee shop. As a first step in the process, the manger 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.

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.

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 of 2, 4, 6, 8, and 10.

c) Do a 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 α = 0.05 for your test.

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.

I'm aware that you don't have the data file but I don't just want the answers. If you could provide a step by step solution without numbers and formulas within excel that would be great. Feel free to make up numbers of your own if it helps you explain.

Can provide the data file if need be.

Number of Arrivals at StarBuckes Coffee Shop
5
3
2
7
10
4
5
7
7
7
10
7
6
10
9
5
9
7
9
6
8
5
9
9
3
6
6
8
2
11
7
6
4
9
4
5
1
4
6
6
7
4
10
3
9
6
9
5
10
7
4
3
6
4
7
6
2
7
4
6
5
5
4
3
4
8
10
4
7
9
5
12
8
5
10
7
12
8
8
7
6
2
4
7
4
5
5
5
4
5
4
6
5
4
5
5
6
5
8
5
5
7
1
6
5
6
7
1
5
5
9
8
2
4
8
7
8
9
3
7
4
8
5
2
8
7
5
8
5
4
6
7
3
3
4
6
10
4
4
5
7
5
4
7
4
5
4
5
2
1
10
9
4
4
8
5
4
5
3
9
8
4
5
9
8
2
7
9
7
6
3
4
7
5
0
5
11
4
9
5
8
3
5
8
9
6
5
5
7
5
8
6
6
4
8
4
2
4
6
5
5
5
10
7
4
5
6
3
1
10
6
4
8
3
9
9
2
5
3
6
4
3
3
4
9
8
3
5
8
7
8
9
3
7
2
5
2
12
10
3
3
4
8
8
10
4
8
6
6
4
7
4
8
7
8
7
8
8
10
7
13
7
13
1
7
6
9
7
4
7
4
0
7
9
5
3
3
4
4
9
13
11
3
3
9
4
9
4
8
7
1
1
6
12
11
1
7
6
1
6
9
7
0
7
6
1
5
7
13
7
10
3
8
0
6
14
3
13
12
11
10
3
11
11
6
11
1
13
13
7
12
2
5
3
5
11
4
9
1
1
7
13
0
2
4
10
6
14
8
10
4
14
0
10
3
8
0
2
9
14
2
4
6
8
7
8
1
11
11
2
7
8
8
6
3
8
0
3
11
8
2
11
3
9
10
8
8
1
5
13
1
3
0
8
12
14
6
8
4
7