The expansion of the Istanbul International Airport has drawn media attention for its revolutionised baggage service which shortened the time a passenger needed to collect his or her baggage. To gauge the performance of its newly-installed baggage carousel, the department of aviation services has collected a random dataset on the number of bags per minute handled by Baggage Carousel A and Baggage Carousel B. These are two different carousels. You would like to summarise the dataset, compare the two carousels and report to the department of aviation services. (The dataset is given in the third sheet named “Baggage carousel” in the provided Excel file Data.xlsx). Your answers should address the following:

1. Choose appropriate graphs to visualise the dataset and provide relevant descriptive statistics and a brief commentary.

2. Compute the average time a passenger needs to wait to see the next piece of baggage. State the assumption you need to make this computation. Hint: what is the assumption behind modelling inter-arrival waiting time as an exponentially distributed variable?

3. Based on your assumptions for both carousels, compute (a) the probability that in one minute there are less than 7 bags and (b) the probability that in one minute there are less than 10 bags. Compare your computed results to what you observe from the data.

4. Explain why you do or do not think your assumption is valid for this dataset.

Baggage Carousel A
Operation Minute ID	Number of baggages
Minute 1	11
Minute 2	15
Minute 3	10
Minute 4	12
Minute 5	8
Minute 6	17
Minute 7	11
Minute 8	11
Minute 9	13
Minute 10	14
Minute 11	10
Minute 12	14
Minute 13	15
Minute 14	16
Minute 15	6
Minute 16	12
Minute 17	9
Minute 18	6
Minute 19	7
Minute 20	11
Minute 21	13
Minute 22	17
Minute 23	9
Minute 24	15
Minute 25	14

Baggage Carousel B
Operation Minute ID	Number of baggages
Minute 1	10
Minute 2	9
Minute 3	11
Minute 4	7
Minute 5	8
Minute 6	15
Minute 7	6
Minute 8	8
Minute 9	10
Minute 10	18
Minute 11	11
Minute 12	17
Minute 13	9
Minute 14	17
Minute 15	18
Minute 16	13
Minute 17	4
Minute 18	13
Minute 19	9
Minute 20	14
Minute 21	17
Minute 22	7
Minute 23	17
Minute 24	11
Minute 25	12