uppose the managers of a coffee shop record the length of time that customers wa
ID: 3075425 • Letter: U
Question
uppose the managers of a coffee shop record the length of time that customers wait in line at the drive-through. The anagers have observed that the mean wait time is 4.0 min. Most customers are served in less than five minutes, but some ave to wait longer. Additionally, the managers have noticed that 8% of all drive-through customers order food with eir beverages lentify the distributions related to this data shown in each histogram. 400 200 150 100 50 200 100 0.0 0.2 0.4 0.6 300 250 200 150 100 100 0 0 10 0.1 0.2 0.3 0.4Explanation / Answer
1) The distribution of wait time for 1000 randomly selected drive-through custmers will have gamma distribution. It is given that mean of the wait time is 4 minutes. So it is expected that second graph will represent the actual picture.
2 & 3) The distribution of proportion of customers who ordered food with their beverages for 1000 random samples with size 10 and with size 50 from population of all drive-through customers will be between graph 1 or graph 4 as for only those graphs x-axis has value between 0 and 1 which represents proportion.As we know distribution of proportion will have smaller variance when sample size increases. So between graph 1 and 4 graph 1 has more sample variance than graph 4 so graph 1 will represent the distribution of proportion of customers who ordered food with their beverages for 1000 random samples with size 10 and graph 4 will represent The distribution of proportion of customers who ordered food with their beverages for 1000 random samples with size 50.
4) The distribution of sample mean wait time for 1000 random samples of size 50 from the population of all drive-through customers will have also have gamma distribution with same mean but with smaller variance than actual wait time distribution. So this will be depicted by graph 3 which has mean time time 4 minutes but with smaller variance.
5) The distribution of sample variances for 1000 random samples of size 50 from the population of all drive-through customers will have distribution with shifted mean which clearly depicts in graph 5.
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