Question
Your friend Bob works part-time at a local supermarket. The supermarket he works at has one express lane open from 5 to 6 PM on
Your friend Bob works part-time at a local supermarket. The supermarket he works at has one express lane open from 5 to 6 PM on weekdays (Monday through Friday). This time of the day is usually the busiest since people tend to stop on their way home from work to buy groceries. The number of items allowed in the express lane is limited to 10 so that the average time to process an order is fairly constant at about 1 minute. The manager of the supermarket notices that there is frequently a long line of people waiting and hears customers grumbling about the wait. To improve the situation, he decides to open additional express lanes during this time period. If he does, however, he will have to "pull" workers from other jobs around the store to serve as cashiers. Hence, he is reluctant to open more lanes than necessary. The manager asks Bob to help him decide how many express lanes to open. His requirement is that there should be no more than one person waiting in line 95% of the time. To help Bob with this task, you set out to study the problem first. You start by counting the number of customer arrival in the express lane on a Monday from 5 to 6pm. There is a total of 81 arrivals. You repeat the experiment on the following four days (Tuesday through Friday) and note the total arrivals of 68, 72, 61 and 66 customers, respectively. One can assume that the customers arrive at the store independently, and they are independently and equally likely to join any of the express lane if there are more than one express lane open. Based on the information above, can you help Bob determine how many express lanes to open
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