During the morning hours at a catalog sales department, telephone calls come in at the rate (Poisson) of 44 per hour. Calls that cannot be answered immediately are put on hold. The system can handle 7 callers on hold. If additional calls come in, they receive a busy signal. The 3 customer service representatives who answer the calls spend an average of 3 minutes with a customer. Use Table 18.4 . a. What is the probability that a caller will get a busy signal? (Hint : Solve for log K or ln K using trial and error.) (Do not round intermediate calculations. Round your answer to 5 decimal places.)
Probability = _________________ (5 decimal places) b. What is the probability that a customer will be put on hold? (Do not round intermediate calculations. Round your answer to 3 decimal places.)
TABLE 18.4 Infinite-source values for Lq and Po given Mu and M Wu M Lq Po WH M L Lq Po My M Lq Po 0.15 1 0.026 .850 1.1 2 0.477 290 6 0.021 2 0.001 .$60 3 0.066 327 2.4 3 2.589 0.20 1 0.050 .800 4 0.011 .332 4 0.431 083 2 0.002 SIS 1.2 2 0.675 .250 5 0.105 089 0.25 1 0.083 .750 3 0.094 294 6 0.027 2 0.004 778 4 0.016 .300 7 0.007 0.30 1 0.129 700 5 0.003 301 2.5 3 3.511 2 0.007 739 1.3 2 0.951 212 4 0.533 074 0.35 1 0.188 650 3 0.130 264 5 0.130 0SO 2 0.011 .702 4 0.023 271 6 0.034 082 0.40 1 0.267 .600 5 0.004 272 7 0.009 2 0.017 .667 1.4 2 1.345 .176 2.6 3 4.933 0.45 1 0.368 .550 3 0.177 .236 4 0.658 0.024 633 4 0.032 245 5 0.161 3 0.002 637 5 0.006 246 6 0.043 074 0.50 1 0.500 500 1.5 2 1.929 .143 7 0.011 2 0.033 600 3 0.237 211 2.7 3 7.354 3 0.003 606 4 0.045 .221 4 0.811 0.55 1 0.672 450 5 0.009 223 5 0.198 2 0.045 569 1.6 2 2.844 .111 6 0.053 067 3 0.004 576 3 0.313 .187 7 0.014 067 0.60 1 0.900 400 4 0.060 .199 2.8 3 12.273 2 0.059 .538 5 0.012 .201 4 1.000 3 0.006 548 1.7 7 2 4.426 081 5 0.241 0.65 1 1.207 350 3 0.409 166 6 0.066 060 2 0.077 509 4 0.080 180 7 0.018 061 0.00S .521 5 0.017 .182 2.9 3 27.193 00 0.70 1 1.633 300 1.8 2 7.674 053 4 1.234 2 0.098 481 3 0.532 146 5 0.293 3 0.011 495 4 0.105 162 6 0.081 054 250 5 0.023 165 7 0.023 2 0.123 455 1.9 2 17.587 026 3.0 4 1.528 3 0.015 471 3 0.6SS .128 5 0.354 0.80 1 3.200 200 4 0.136 .145 6 0.099 2 0.152 429 5 0.030 .149 7 0.028 050 3 0.019 447 6 0.007 .149 S 0.008 05 0.85 1 4.817 150 2.0 3 0.889 .111 3.1 4 1.902 2 0.187 404 4 0.174 .130 5 0.427 3 0.024 425 5 0.040 .134 6 0.120 04 4 0.003 427 6 0.009 .135 7 0.035 045 0.90 1 8.100 100 2.1 3 1.149 096 $ 0.010 045 2 0.229 .379 4 0.220 117 3.2 4 2.386 027 3 0.030 403 5 0.052 .121 5 0.513 4 0.004 406 6 0.012 .122 6 0.145 0.95 1 18.050 050 2.2 3 1.491 081 7 0.043 2 0.277 .356 0.277 .105 $ 0.012 04 3 0.037 383 5 0.066 .109 3.3 4 3.027 023 4 0.005 386 6 0.016 .111 5 0.615 1.0 2 0.333 333 2.3 3 1.951 .068 6 0.174 3 0.045 364 4 0.346 093 7 0.052 0.007 .367 5 0.084 099 $ 0.015 1 4 3.906 019 4.3 7 0.289 130 5.2 6 4.301 003 0.737 029 $ 0.097 .013 7 1.081 6 0.209 032 9 0.033 014 S 0.36S 0.063 033 10 0.011 014 9 0.135 6 0.019 033 4.4 5 5.268 006 10 0.049 4 5.165 015 6 1.078 010 11 0.018 006 5 0.882 026 7 0.337 012 5.3 6 5.303 6 0.248 029 $ 0.114 012 7 1.249 0.076 030 9 0.039 012 $ 0.422 005 8 0.023 030 10 0.013 012 9 0.155 9 0.007 030 4.5 5 6.62 005 10 0.057 005 3.6 7.090 .01 1 6 1.265 009 11 0.021 1.055 023 7 0.391 010 12 0.007 6 0.295 026 $ 0.134 011 5.4 6 6.661 0.019 027 9 0.046 .011 7 1.444 $ 0.028 027 10 0.015 .011 $ 0.483 004 9 0.008 027 4.6 5 9.289 004 9 0.178 004 3.7 4 10.347 .00S 6 1.487 .00S 10 0.066 5 1.265 020 7 0.453 009 11 0.024 6 0.349 023 S 0.156 010 12 0.009 7 0.109 024 9 0.054 010 5.5 6 8.590 002 $ 0.034 025 10 0.018 010 7 1.674 003 0.010 025 4.7 5 13.382 003 S 0.553 38 4 16.937 005 6 1.752 007 9 0.204 1.519 017 7 0.525 .008 10 0.077 004 6 0.412 021 $ 0.181 009 11 0.028 004 7 0.129 022 9 0.064 009 12 0.010 $ 0.041 022 10 0.022 009 5.6 6 11.519 .001 9 0.013 022 4.8 5 21.641 002 7 1.944 9 4 36.859 .002 6 2.071 006 S 0.631 003 51.830 015 7 0.607 .00S 9 0.233 004 6 0.485 019 $ 0.209 00S 10 0.088 7 0.153 020 9 0.074 .008 11 0.033 $ 0.050 020 10 0.026 008 12 0.012 9 0.016 020 4.9 5 46.566 001 5.7 6 16.446 001 4.0 5 2.216 013 6 2.459 005 7 2.264 002 6 0.570 017 7 0.702 007 S 0.721 7 0.180 018 8 0.242 007 9 0.266 $ 0.059 018 9 0.087 007 10 0.102 0.019 .0IS 10 0.031 007 11 0.03S 5 2.703 011 11 0.011 007 12 0.014 003 6 0.668 015 5.0 6 2.938 005 5.8 6 26.373 001 7 0.212 016 7 0.$10 006 7 2.645 $ 0.070 016 $ 0.279 006 $ 0.823 0.023 017 9 0.101 007 9 0.303 4.2 5 3.327 009 10 0.036 007 10 0.116 003 6 0.784 013 11 0.013 007 11 0.044 7 0.248 014 5.1 6 3.536 004 12 0.017 $ 0.053 015 7 0.936 005 5.9 6 56.300 000 9 0.027 015 $ 0.321 006 7 3.113 002 10 0.009 015 9 0.117 006 $ 0.939 002 4.3 5 4.149 00S 10 0.042 006 9 0.345 0.919 .012 11 0.015 006 10 0.133
