Question 3 (2+2+3+3+5 = 15 points) atlantic video, a small video rental store in philadelphia, is open 24 hours a day, and-due to its proximity to a major business school-experiences customers arriving around the clock. a recent analysis done by the store manager indicates that there are 30 customers arriving every hour, with a standard deviation of interarrival times of 2 minutes. this arrival pattern is consistent and is independent of the time of day. the checkout is currently operated by one employee, who needs on average 1.7 minutes to check out a customer. the standard deviation of this check-out time is 3 minutes, primarily as a result of customers taking home different numbers of videos.

if you assume that every customer rents at least one video (i. e., has to go to the checkout), what is the average time a customer has to wait in line before getting served by the checkout employee (i. e., waiting time in queue)?

Each of the following data sets has a mean of x = 10. (i) 8 9 10 11 12 (ii) 7 9 10 11 13 (iii) 7 8 10 12 13 (a) without doing any computations, order the data sets according to increasing value of standard deviations. (i), (iii), (ii) (ii), (i), (iii) (iii), (i), (ii) (iii), (ii), (i) (i), (ii), (iii) (ii), (iii), (i) (b) why do you expect the difference in standard deviations between data sets (i) and (ii) to be greater than the difference in standard deviations between data sets (ii) and (iii)? hint: consider how much the data in the respective sets differ from the mean. the data change between data sets (i) and (ii) increased the squared difference îł(x - x)2 by more than data sets (ii) and (iii). the data change between data sets (ii) and (iii) increased the squared difference îł(x - x)2 by more than data sets (i) and (ii). the data change between data sets (i) and (ii) decreased the squared difference îł(x - x)2 by more than data sets (ii) and (iii). none of the above