A bank manager has developed a new system to reduce the time customers spend waiting to be served by tellers during peak business hours. Typical waiting times during peak business hours under the current system are roughly 9 to 10 minutes. The bank manager hopes that the new system will lower typical waiting times to less than six minutes and wishes to evaluate the new system. When the new system is operating consistently over time, the bank manager decides to select a sample of 100 customers that need teller service during peak business hours. Specifically, for each of 100 peak business hours, the first customer that starts waiting for teller service at or after a randomly selected time during the hour will be chosen. In Exercise 7.5 we will discuss how to obtain a randomly selected time during an hour. When each customer is chosen, the number of minutes the customer spends waiting for teller service is recorded. The 100 waiting times that are observed are given in Table 1.8.

Using the data, estimate limits between which the waiting times of most of the customers arriving during peak business hours would be. Also, estimate the proportion of waiting times of customers arriving during peak business hours that are less than six minutes.

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TABLE Waiting Times (in Minutes) for the Bank Customer Waiting Time Case 1.8 1.6 6.6 5.6 6.2 5.4 4.9 5.4 .8 3.2 7.2 7.3 2.3 4.5 7.2 10.7 4.1 5.6 7.9 6.1 3.8 6.5 44 1.1 8.7 6.7 2.9 4.7 8. 9.1 3.6 4.3 7.7 2.7 2.2 4.0 3.7 5.8 1.4 4 8.6 7.8 6.8 10.2 2.0 5.2 2.8 8.0 8.4 9.5 6.3 4.3 1.3 4.4 4.8 5.2 5.8 9.9 7.4 7.5 6.7 7.0 3.5 5.3 6.3 4.5 4.3 4.5 3.8 1.8 51 3.7 5.5 4.0 5.7 2.4 9.2 5.0 3.9 4.6 2. 6.5 8.3 6.4 8.6 4.2 5.8 3.4 9.3 10.9 7.4 1.8 6.1 6.3 9.8 2.9 11.6 4.7 3.9 3.1