Problem 18-9 One field representative services five customers for a computer manufacturer. Customers request assistance at an average (Poisson- distributed) rate of once every four working days. The field representative can handle an average (Poisson-distributed) of one call per day. Determine: Use Table 1. a. The expected number of customers waiting. (Round your answer to 3 decimal places.) Expected number of customers waiting b. The average length of time customers must wait from the initial request for service until the service has been completed. (Round your answer to 2 decimal places.) Average length of time days c. The percentage of time the service rep will be idle. (Round your answer to 1 decimal place.) Percentage of Idle time d. By how much would your answer to part a be reduced if a second field rep were added? (Round your answer to 3 decimal places.) Reduced number of customer(s) X M D F x M D Fx M D F x M D F TABLE 18.7 Finite-queuing tables Population 5 .125 2.082.994.260 3.058 .994.440 .012 1.060 999 1.575.920 2 .303 .950 .0191 .095 998 .130 2.089.933 1 .903 .695 20251 .125.997 1 594 914 270 3.064.994 460 .030 1 .149 996 .1352 .095933 2 .323.944 .034 1 .169.995 1 .612.907 1 .915.677 .036 .179 994.140 2.102.992.280 3.071.993 .040 1 .199 993 1.630.900 2 .342.938.480 .042 1 1 208 992 .145 3 .011.999 1 .925661 .044 1 .218.991 2 .109 .991 .290 4.007 .999 .046 1 .228 990 1 .647 892 3.079.992 .050 1 .247 .989 .150 3.012.999 2 362.932 500 .052 1 .257 988 2 .115 990 1 .934 644 .054 1 .266 987 1.664 885 .300 4.008 .999 .056 2 .018 999.155 3 .013 .999 3.086.990 1 276 985 2.123.989 2 382.926 520 .058 2 .019 999 1 .680 .877 1 .942.628 1 .285 984.160 3.015 .999 .310 4.009 .999 .0602 .020 .999 2.130 988 3 .094 989 1 .295.983 1.695.869 2.402.919.540 .0622 .022 999 .165 3.016 999 1 .950 613 1 304 982 2.137.987 .320 4 .010 .999 .064 2 .023 999 1 .710 861 3.105.988 1 .314 981.170 3.017 999 2.422.912 560 .066 2 .024 999 2.145.985 1 .956.597 1 323 979 1 725 853 330 4 .012999 .068 2 .026 999.180 3.021.999 3.112.986 1 .353 978 2 .161983 2 .442.904.580 .070 2 .027 999 1 752 836 1 .962 583 1 .342.977.190 3 .024 998.340 4 .013 .999 .075 2 .031 999 2 117 .980 3 121.985 1 365 973 1.778 819 2.462.896.600 .080 2 .035 998 200 3 .028 998 1 .967569 1 388 969 2 .194 976.360 4.017 998 .0852 040 998 1 .801 801 3.141.981 1 .410.965 210 3.032.998 2.501.880.650 .090 2 .044 998 2 211.973 1 .975 542 1 1 432.960 1.822.783.380 4 .021 998 .095 2 .049 997 220 3 .036 .997 3 163 976 1 .454 955 2 .229.969 2 .540.863.700 100 2 .054 997 1 .842.765 1 .981 516 1 475 950 230 3.041.997.400 4 .026 997 .105 2 .059.997 2 247 965 3.186.972 1 496 945 1 860 747 2 .579.845.750 .110 2 .065 996 240 3 .046 .996 1 .986 493 1 .516 939 2 .265.960.4204 .031.997 .115 2 .017 995 1 876 730 3 .211 966.800 1 537 933 .250 3 .052 995 2.616 826 .1202 .076 .995 2 .284.955 1 1 .989.471 1 .556 927 1 .890 712.440 4 .037.996 3 .238 960 2.652 807 1992.451 4 .045 .995 3 .266 953 2 .686 787 1994.432 4 .053.994 3.296.945 2 .719 767 1996.415 4.063 992 3 327 936 2 .750 748 1.997 399 4 073 991 .359.927 2 .779 728 1.998 384 4 .085.999 3 392 917 2 .806 708 1998 370 4.098 986 3 426 906 2 831 689 1.999 357 4 .113 984 3 461 895 2.854 .670 1 .999.345 4 .130 981 3.497 883 2 .875.652 1 .999 355 4 .179.972 3.588 850 2 .918 608 1999 308 4 .240 960 3.678 .815 2 .950 568 1.999.286 4 316 944 3 .763 777 2.972 532 4 410 924 3.841 739 2.987.500 (continued)