18-5

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Problem 18-5 (Algo) A small town with one hospital has 3 ambulances to supply ambulance service. Requests for ambulances during nonholiday weekends average 0.62 per hour and tend to be Poisson-distributed. Travel and assistance time averages 2.10 hours per call and follows an exponential distribution Use Table 18.4 a. Find system utilization. (Round your answer to the nearest whole percent.) System utilization % b. Find the average number of customers waiting. (Round your answer to 3 decimal places.) Average number of customers c. Find the average time customers wait for an ambulance. (Round your answer to 3 decimal places.) Average time hour c. Find the average time customers wait for an ambulance. (Round your answer to 3 decimal places.) Average time hour d. Find the probability that all ambulances will be busy when a call comes in. (Round calculations to 3 decimal places and final answer to 2 decimal places.) ediate Probability TABLE 18.4 Infinite-source values for Lg and Po given Ny and M / La Lg Lq Po 0.15 1 0.026 850 1.1 2 0.477 290 6 0.021 100 2 0.001 S60 3 0.066 327 2.4 3 2.589 056 0.20 ! 0.050 SOO 4 0.011 332 4 0.431 OS 3 2 0.002 SIS 1.2 2 0.675 250 5 0.105 089 0.25 ! 0.083 .750 3 0.094 294 6 0.027 090 2 0.004 775 4 0.016 300 7 0.007 091 0.30 1 0.129 700 5 0.003 301 2.5 3 3.511 .045 2 0.007 739 1.3 2 0.951 212 4 0.533 .074 035 1 0.1SS 650 3 0.130 264 $ 0.130 OSO 2 0.011 702 4 0.023 271 6 0.034 052 0.40 1 0.267 600 5 0.004 272 7 0.009 OS2 2 0.017 667 1.4 2 1.345 1762.6 3 4.933 035 0.45 1 0.368 550 3 0.177 236 4 0.658 065 2 0.024 633 0.032 245 5 0.161 072 3 0.002 637 4 5 2 0.006 246 6 0.043 074 0.50 1 0.500 500 1.5 1929 143 7. 0.011 074 2 0.033 600 3 0.237 211 2.7 3 7.354 025 3 0.003 606 4 0.045 221 4 0.811 057 0.55 1 0.672 450 5 0.009 223 5 0.198 065 2 0.045 569 1.6 2 2.344 6 0.053 067 3 0.001 576 3 0.313 187 7 0.014 067 0.60 1 0.900 400 4 0.000 1992.8 3 12 273 016 2 0.059 538 5 0.012 201 4 1.000 050 3 0.006 548 7 4.426 OSI 5 0.341 058 2 3 0.65 1 1.207 350 0.409 166 6 0.066 060 2 0.077 509 0.030 ISO 7 0.01S 061 3 0.005 521 5 0.017 1822.9 3 27.193 008 0.70 1 1.633 300 IS 2 7.674 053 1.234 044 2 0098 451 3 0.532 146 5 0.293 OS2 MAS 105 161 0.70 1 1.633 300 1.5 2 7.674 053 4. 1.234 044 2 0.098 481 3 0.532 146 5 0.293 052 3 0.011 495 4 0.105 162 6 0.031 054 0.75 1 2.250 250 5 0.023 .165 7 0.023 .055 2 0.123 455 1.9 2 17557 026 3.0 4 1.528 03S 3 0.015 471 0.68S 125 5 0.354 047 3 4 0.30 3.200 200 0.136 145 6 0.099 049 2 0.152 429 5 0.030 149 7 0.025 050 3 0.019 447 6 0.007 149 S 0.008 050 0.85 1 4.817 150 2.0 3 0.889 13.1 4 1.902 032 2 0.187 404 4 0.174 130 0.427 042 5 6 3 0.024 425 5 0.010 134 0.120 044 4 0.003 427 6 0.009 135 7 0.035 045 0.90 1 S. 100 100 2.1 3 1.149 096 S 0.010 045 2 0.229 379 4 0.220 117 3.2 4 2.356 027 3 0.030 403 5 0.052 121 5 0.513 037 4 0.004 406 6 0.012 122 0.145 040 0.95 1 ISO50 050 2.23 1.491 OSI 7 0.043 040 2 0.277 356 0.277 105 S 0.012 041 + 5 3 0.037 333 0.066 109 3.3 4 3.027 023 4 0.005 336 6 0.016 111 5 0.615 033 1.0 2 0.333 333 2.3 3 1.951 068 6 0.174 0.36 3 0.045 364 4 0.346 093 7 0.052 037 4 0.007 367 5 0.054 099 S 0.015 037 3.4 4 3.906 019 4.3 7 0259 13052 4.301 .003 5 0.737 020 0.097 013 7 1.051 005 6 0.209 032 9 0.033 014 S 0 365 005 7 0.063 033 10 0.011 014 9 0.135 005 S 0.019 033 4.4 5 5.268 006 10 0.049 005 3.5 5.165 015 6 1.073 010 0.015 006 5 0.832 026 7 0.337 012 5.3 6 5 303 003 6 0.248 029 0.114 012 7 1.249 001 3.5 4 5.165 2015 6 1.078 010 11 0.018 .006 5 0.882 026 7 0.337 .0125.3 6 5.303 2003 6 0.248 .029 S 0.114 012 7 1.249 .004 7 0.076 030 9 0.039 .012 S 0.422 .005 S 0.023 .030 10 0.013 012 9 0.155 .005 9 0.007 .030 4.5 5 6.862 005 10 0.057 005 3.6 4 7.090 .011 6 1.265 .009 11 0.021 .005 5 1.055 .023 7 0.391 010 12 0.007 005 6 0.295 026 S 0.134 011 5.4 6 6.661 .002 7 0.019 027 9 0.046 011 7 1.444 004 S 0028 027 10 0.015 011 CD 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 0.066 004 5 1 265 020 7 0.453 .009 11 0.024 .005 6 0.349 .023 0.156 010 12 0.009 005 S 9 7 0.109 024 0.054 010 5.5 6 S.590 .002 Op 0.034 025 10 0.018 010 7 1.674 003 9 0.010 025 4.7 5 13.382 003 S 0.553 2004 3.5 4 16.937 005 6 1.752 .007 9 0.204 .004 5 1.519 017 7 0.525 .OOS 10 0.077 .004 6 0.412 .021 S 0.181 .009 0.025 004 7 0.129 022 9 0.064 009 12 0.010 .004 S 0041 .022 10 0.022 009 5.6 6 11.519 001 9 0.013 022 4.8 5 21.641 002 7 1.944 .003 3.9 36.859 002 6 2.071 006 S 4 5 0.631 .003 1.830 015 7 0.607 008 9 0.233 004 6 0.485 019 S 0.209 .008 10 0.083 004 7 0.153 020 9 0.074 OOS 0.033 004 S 0.050 020 10 0026 008 12 0.012 004 18.4.png S 0.034 025 10 0.018 010 7 1.674 .003 9 0.010 5 025 4.7 005 .004 3.5 4 13 352003 1.752 .007 16.937 6 S 0.553 90.204 004 5 1.519 LIO 7 0.525 800 10 0.077 004 6 0.412 021 S 0.181 600 0.025 004 7 0.129 022 9 0.064 600 12 0.010 004 S 0.001 022 10 0.022 00956 6 11.519 .001 9 0.013 022 4.5 5 21 641.002 7 1.944 003 3.9 + 36 859 002 6 2071 000 S 0631 003 5 1.830 SIO 7 0.607 00S 9 0.233 004 6 0.455 610 S 0.209 005 10 0.0SS 004 7 0.153 020 6 0.074 005 11 0.033 004 S 0.050 020 10 0.026 800 12 0.012 0044 9 0.016 020 49 46.566 001 5.7 6 16 446001 $ 6 4.0 5 2.216 013 2.459 005 7 2.264 .002 9 0.570 017 7 0.702 007 CO 0.721 003 7 0.150 SIO S 0.242 007 9 0.266 .003 0 059 SIO 9 0.087 007 10 0.102 003 6 0.019 SIO 10 0.031 007 11 SEO O 003 4.1 5 2.703 TIO 11 0.011 007 12 0.014 003 6 0668 015 5.0 6 2.938 005 5.8 6 26.373 100 7 0.212 016 7 0.310 900 7 2.648 002 0.070 016 S 0.279 .006 8 0.823 003 9 0.023 017 0.101 007 9 0.303 003 4.2 3 3.327 009 10 9 0 007 10 0.116 003 6 0 734 ETO 11 0.013 007 11 0.044 003 7 0.248 014 5.1 6 3.536 004 12 0.017 003 S 0053 015 7 0.936 0055.9 6 56.300 .000 9 0.027 015 S 0.321 900 7 CHI'S 002 10 0.009 .015 9 0.117 006 S 0.939 002 5 4.149 008 10 0.042 000 9 0.3-45 003 6 0.919 012 11 0.015 006 10 0.133 003