Question 3.

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 Minute 26 20 Minute 27 11 Minute 28 17 Minute 29 16 Minute 30 8 Minute 31 19 Minute 32 11 Minute 33 6 Minute 34 11 Minute 35 9 Minute 36 8 Minute 37 12 Minute 38 17 Minute 39 12 Minute 40 10 Minute 41 13 Minute 42 19 Minute 43 15 Minute 44 8 Minute 45 12 Minute 46 8 Minute 47 13 Minute 48 14 Minute 49 12 Minute 50 7 Minute 51 11 Minute 52 13 Minute 53 11 Minute 54 17 Minute 55 12 Minute 56 13 Minute 57 9 Minute 58 13 Minute 59 15 Minute 60 16 Minute 61 15 Minute 62 9 Minute 63 13 Minute 64 13 Minute 65 14 Minute 66 15 Minute 67 12 Minute 68 12 Minute 69 8 Minute 70 9 Minute 71 Minute 72 Minute 73 Minute 74 Minute 75 Minute 76 Minute 77 Minute 78 Minute 79 Minute 80 Minute 81 Minute 82 Minute 83 Minute 84 Minute 85 Minute 86 Minute 87 Minute 88 Minute 89 Minute 90 Minute 91 Minute 92 Minute 93 Minute 94 Minute 95 Minute 96 Minute 97 Minute 98 Minute 99 Minute 100 Minute 101 Minute 102 Minute 103 Minute 104 Minute 105 Minute 106 Minute 107 Minute 108 Minute 109 Minute 110 Minute 111 Minute 112 Minute 113 Minute 114 Minute 115 Minute 116 Minute 117 Minute 118 Minute 119 Minute 120 Minute 121 Minute 122 Minute 123 Minute 124 Minute 125 Minute 126 Minute 127 Minute 128 Minute 129 Minute 130 Minute 131 Minute 132 Minute 133 Minute 134 Minute 135 Minute 136 Minute 137 Minute 138 Minute 139 Minute 140 9 9 14 18 10 5 16 16 14 16 9 12 4 6 14 18 5 9 7 8 11 17 7 11 6 12 13 10 19 8 12 8 11 15 19 13 9 13 19 9 6 14 6 12 9 12 10 14 9 8 8 16 10 9 10 7 10 10 14 12 14 13 11 11 17 17 12 14 16 12 Minute 141 Minute 142 Minute 143 Minute 144 Minute 145 Minute 146 Minute 147 Minute 148 Minute 149 Minute 150 Minute 151 Minute 152 Minute 153 Minute 154 Minute 155 Minute 156 Minute 157 Minute 158 Minute 159 Minute 160 Minute 161 Minute 162 Minute 163 Minute 164 Minute 165 Minute 166 Minute 167 Minute 168 Minute 169 Minute 170 Minute 171 Minute 172 Minute 173 Minute 174 Minute 175 Minute 176 Minute 177 Minute 178 Minute 179 Minute 180 Minute 181 Minute 182 Minute 183 Minute 184 Minute 185 Minute 186 Minute 187 Minute 188 Minute 189 Minute 190 Minute 191 Minute 192 Minute 193 Minute 194 Minute 195 Minute 196 Minute 197 Minute 198 Minute 199 Minute 200 9 11 20 5 13 13 12 12 10 9 14 14 12 10 19 7 13 14 10 15 11 11 12 19 11 9 11 15 7 10 10 14 13 12 13 16 9 9 10 10 20 8 8 13 12 19 7 5 15 13 12 14 8 8 14 18 14 8 10 20 Average 11.89 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 Minute 26 20 Minute 27 11 Minute 28 17 Minute 29 16 Minute 30 8 Minute 31 19 Minute 32 11 Minute 33 6 Minute 34 11 Minute 35 9 Minute 36 8 Minute 37 12 Minute 38 17 Minute 39 12 Minute 40 10 Minute 41 13 Minute 42 19 Minute 43 15 Minute 44 8 Minute 45 12 Minute 46 8 Minute 47 13 Minute 48 14 Minute 49 12 Minute 50 7 Minute 51 11 Minute 52 13 Minute 53 11 Minute 54 17 Minute 55 12 Minute 56 13 Minute 57 9 Minute 58 13 Minute 59 15 Minute 60 16 Minute 61 15 Minute 62 9 Minute 63 13 Minute 64 13 Minute 65 14 Minute 66 15 Minute 67 12 Minute 68 12 Minute 69 8 Minute 70 9 Minute 71 Minute 72 Minute 73 Minute 74 Minute 75 Minute 76 Minute 77 Minute 78 Minute 79 Minute 80 Minute 81 Minute 82 Minute 83 Minute 84 Minute 85 Minute 86 Minute 87 Minute 88 Minute 89 Minute 90 Minute 91 Minute 92 Minute 93 Minute 94 Minute 95 Minute 96 Minute 97 Minute 98 Minute 99 Minute 100 Minute 101 Minute 102 Minute 103 Minute 104 Minute 105 Minute 106 Minute 107 Minute 108 Minute 109 Minute 110 Minute 111 Minute 112 Minute 113 Minute 114 Minute 115 Minute 116 Minute 117 Minute 118 Minute 119 Minute 120 Minute 121 Minute 122 Minute 123 Minute 124 Minute 125 Minute 126 Minute 127 Minute 128 Minute 129 Minute 130 Minute 131 Minute 132 Minute 133 Minute 134 Minute 135 Minute 136 Minute 137 Minute 138 Minute 139 Minute 140 9 9 14 18 10 5 16 16 14 16 9 12 4 6 14 18 5 9 7 8 11 17 7 11 6 12 13 10 19 8 12 8 11 15 19 13 9 13 19 9 6 14 6 12 9 12 10 14 9 8 8 16 10 9 10 7 10 10 14 12 14 13 11 11 17 17 12 14 16 12 Minute 141 Minute 142 Minute 143 Minute 144 Minute 145 Minute 146 Minute 147 Minute 148 Minute 149 Minute 150 Minute 151 Minute 152 Minute 153 Minute 154 Minute 155 Minute 156 Minute 157 Minute 158 Minute 159 Minute 160 Minute 161 Minute 162 Minute 163 Minute 164 Minute 165 Minute 166 Minute 167 Minute 168 Minute 169 Minute 170 Minute 171 Minute 172 Minute 173 Minute 174 Minute 175 Minute 176 Minute 177 Minute 178 Minute 179 Minute 180 Minute 181 Minute 182 Minute 183 Minute 184 Minute 185 Minute 186 Minute 187 Minute 188 Minute 189 Minute 190 Minute 191 Minute 192 Minute 193 Minute 194 Minute 195 Minute 196 Minute 197 Minute 198 Minute 199 Minute 200 9 11 20 5 13 13 12 12 10 9 14 14 12 10 19 7 13 14 10 15 11 11 12 19 11 9 11 15 7 10 10 14 13 12 13 16 9 9 10 10 20 8 8 13 12 19 7 5 15 13 12 14 8 8 14 18 14 8 10 20 Average 11.89