A simulation is to be conducted of a job shop that performs two operations: milling and planing, in that order. It would be possible to collect data about processing times for each operation, then generate random occurrences from each distribution. However, the shop manager says that the times might be related; large milling jobs take lots of planing. Data are collected for the next 25 orders, with the following results (Table 2) in minutes: 3 Milling Planing Milling Planing Time Time Time Time Order (Minutes) (Minutes) Order (Minutes) (Minutes) 1 12.3 10.6 14 24.6 16.6 2 20.4 13.9 15 28.5 21.2 18.9 14.1 16 11.3 9.9 4 16.5 10.1 17 13.3 10.7 5 8.3 8.4 18 21.0 14.0 6 6.5 8.1 19 19.5 13.0 7 25.2 16.9 15.0 11.5 8 17.7 13.7 21 12.6 9.9 9 10.6 10.2 22 14.3 13.2 10 13.7 12.1 17.0 12.5 11 26.2 16.0 21.2 14.2 12 30.4 18.9 28.4 19.1 13 9.9 7.7 20 23 24 25 Table 2: Milling and Planing Times a. Plot milling time on the horizontal axis and planing time on the vertical axis. Do these data seem dependent? b. Compute the sample correlation between milling time and planing time c. Fit a bi-variate Normal distribution to these data (i.e., just compute the parameters and write the equation).
