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 6 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.

a. Consider the peak business hours from 2:00 p.m. to 2:59 p.m., from 3:00 p.m. to 3:59 p.m., from 4:00 p.m. to 4:59 p.m., and from 5:00 p.m. to 5:59 p.m. on a particular day. Also, assume that a computer software system generates the following four random numbers between 00 and 59: 32, 00, 18, and 47. This implies that the randomly selected times during the first three peak business hours are 2:32 p.m., 3:00 p.m., and 4:18 p.m. What is the randomly selected time during the fourth peak business hour?
b. 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 1.9. Using the largest and smallest observations in 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.

Transcribed Image Text:

Composite Scores for the Video Game Satisfaction Rating Case oS VideoGame TABLE 1.8 44 39 44 46 44 42 44 45 42 45 47 46 38 45 45 42 40 46 44 43 42 47 43 46 45 41 44 47 48 38 43 43 44 45 42 41 41 45 46 40 45 40 44 43 44 46 40 44 44 41 39 41 44 40 43 38 46 42 39 43 39 45 43 36 41 Waiting Times (in Minutes) for the Bank Customer Waiting Time Case oS WaitTime TABLE 1.9 1.6 6.2 3.2 5.6 7.9 6.1 7.2 6.6 5.4 6.5 4.4 1.1 3.8 7.3 5.6 4.9 2.3 4.5 7.2 10.7 4.1 5.1 5.4 8.7 6.7 2.9 7.5 6.7 3.9 .8 4.7 8.1 9.1 7.0 3.5 4.6 2.5 3.6 4.3 7.7 5.3 6.3 6.5 8.3 2.7 2.2 4.0 4.5 4.3 6.4 6.1 3.7 5.8 1.4 4.5 3.8 8.6 6.3 .4 8.6 7.8 1.8 5.1 4.2 6.8 10.2 2.0 5.2 3.7 5.5 5.8 9.8 2.8 8.0 8.4 4.0 3.4 2.9 11.6 9.5 6.3 5.7 9.3 10.9 4.3 1.3 4.4 2.4 7.4 4.7 3.1 4.8 5.2 9.2 1.8 3.9 5.8 9.9 7.4 5.0