Please show equations!

Problem 2. Resistors for electronic circuits are manufactured on a high-speed automated machine. The machine is set up to produce a large run of resistors of 1,000 ohms each. To set up the machine and to create a control to be used throughout the run, 15 samples were taken with four resistors in each sample. The come list of samples and their measured values are as follows: Sample number Readings (in Ohms) 986 1 2 3 4 5 6 1010 995 990 1015 1013 994 989 1001 1006 992 996 1019 981 999 1013 7 8 991 996 1003 1020 1019 1001 992 986 989 1007 1006 996 991 993 1002 985 1009 1015 1009 1005 994 982 996 1005 1006 997 994 1008 998 993 1005 1020 996 1007 979 989 1011 1003 984 992 9 10 11 12 13 14 15 991 989 988 1005 a. Develop an fchart and R chart and plot the values. X Readings (in Ohms) Readings (in Ohms) X-bar R Sample number 1 2 2 3 4 1010 995 990 R 25 15 25 22 Sample number 1 2 3 3 4 5 991 996 1003 1020 985 1009 1015 1009 986 994 1008 998 0 1015 1013 5 26 991 996 1003 1020 1019 1001 992 986 989 1007 1006 986 994 1008 998 993 1005 1020 996 1007 979 X-bar 993 999 1004 1011 1008 999 996 995 1002 996 997 985 1009 1015 1009 1005 994 982 996 1005 1006 997 6 1005 994 994 993 1005 1010 995 990 1015 1013 994 989 1001 1006 992 996 6 11 38 989 7 0 7 7 8 9 982 996 15 1019 1001 992 986 989 1007 1006 1001 1006 992 996 1005 8 9 9 10 11 18 28 1020 996 1007 979 989 10 1006 997 989 17 0 1011 1004 991 G R Exhibit 10.13 Average of x-bar 1 Average of R Factor for R Chart stochor Clover Az conuerter D. on WN 2. OOOOOOOOOO OOOOOOO GON WAS 0.31 0.33 0.24 0.22 0.2 01 . 0.4 UCLX R-bar ( R) R-bar (R) HE