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A random sample of 105 automobile owners in a region shows that an automobile is driven on average 23,000 kilometers per year with a standard deviation of 3600 kilometers. Assume the distribution of measurements to be approximately normal. Construct a 99​% prediction interval for the kilometers traveled annually by an automobile owner in the region. The prediction interval is______ < Xo < _________

A random sample of 105 automobile owners in a region shows that an automobile is driven on average 23,000 kilometers per year with a standard deviation of 3600 kilometers. Assume the distribution of measurements to be approximately normal. Construct a 99​% prediction interval for the kilometers traveled annually by an automobile owner in the region. The prediction interval is______ < Xo < _________

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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A random sample of 105 automobile owners in a region shows that an automobile is driven on average 23,000 kilometers per year with a standard deviation of 3600 kilometers. Assume the distribution of measurements to be approximately normal. Construct a 99​% prediction interval for the kilometers traveled annually by an automobile owner in the region.

The prediction interval is______ < Xo < _________

​(Round to the nearest integer as​ needed.)

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0.8997 0.9015 1.2 1.3 0.9032 0.9049 0.9066 0.9082 0.9099 0.9115 0.9131 0.9147 0.9162 0.9177 1.3 1.4 0.9192 0.9207 0.9222 0.9236 0.9251 0.9265 0.9279 0.9292 0.9306 0.9319 1.4 1.5 0.9332 0.9345 0.9357 0.9370 0.9382 0.9394 0.9406 0.9418 0.9429 0.9441 1.5 1.6 0.9452 0.9463 0.9474 0.9484 0.9495 0.9505 0.9515 0.9525 0.9535 0.9545 1.6 1.7 0.9554 0.9564 0.9573 0.9582 0.9591 0.9599 0.9608 0.9616 0.9625 0.9633 1.7 1.8 0.9641 0.9649 0.9656 0.9664 0.9671 0.9678 0.9686 0.9693 0.9699 0.9706 1.8 1.9 0.9713 0.9719 0.9726 0.9732 0.9738 0.9744 0.9750 0.9756 0.9761 0.9767 1.9 2.0 0.9772 0.9778 0.9783 0.9788 0,9793 0.9798 0.9803 0.9808 0.9812 0.9817 2.0 2.1 0.9821 0.9826 0.9830 0.9834 0.9838 0.9842 0.9846 0.9850 0.9854 0.9857 2.1 2.2 0.9861 0.9864 0.9868 0.9871 0.9875 0.9878 0.9881 0.9884 0.9887 0.9890 2.2 2.3 0.9893 0.9896 0.9898 0.9901 0.9904 0.9906 0.9909 0.9911 0.9913 0.9916 2.3 2.4 0.9918 0.9920 0.9922 0.9925 0.9927 0.9929 0.9931 0.9932 0.9934 0.9936 2.4 2.5 0.9938 0.9940 0.9941 0.9943 0.9945 0.9946 0.9948 0.9949 0.9951 0.9952 2.5 2.6 0.9953 0.9955 0.9956 0.9957 0.9959 0.9960 0.9961 0.9962 0.9963 0.9964 2.6 0.9965 0.9966 0.9967 0.9968 0.9969 0.9970 0.9971 0.9972 0.9973 0.9974 2.7 2.8 0.9974 0.9975 0.9976 0.9977 0.9977 0.9978 0.9979 0.9979 0.9980 0.9981 2.8 2.9 0.9981 0.9982 0.9982 0.9983 0.9984 0.9984 0.9985 0.9985 0.9986 0.9986 2.9 3.0 0.9987 0.9987 0.9987 0.9988 0.9988 0.9989 0.9989 0.9989 0.9990 0.9990 3.0 3.1 0.9990 0.9991 0.9991 0.9991 0.9992 0.9992 0.9992 0.9992 0.9993 0.9993 3.1 3.2 0.9993 0.9993 0.9994 0.9994 0.9994 0.9994 0.9994 0.9995 0.9995 0.9995 3.2 3.3 0.9995 0.9995 0.9995 0.9996 0.9996 0.9996 0.9996 0.9996 0.9996 0.9997 3.3 3.4 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9998 3.4 .01 .02 .03 .04 .05 .06 .07 .08 .09 .08 .09 0.5319 0.5359 0.0 2 Z
Critical Values of the t-Distribution Critical Values of the t-Distribution a a 0.40 0.30 0.20 0.15 0.10 0.05 0.025 0.02 0.015 0.01 0.0075 0.005 0.0025 0.0005 1 0.325 0.727 1.376 1.963 3.078 6.314 12.706 1 15.894 21.205 31.821 42.433 63.656 127.321 636.578 2 0.289 0.617 1.061 1.386 1.886 2.920 4.303 2 4.849 5.643 6.965 8.073 9.925 14.089 31.600 3 0.277 0.584 0.978 1.250 1.638 2.353 3.182 3 3.482 3.896 4.541 5.047 5.841 7.453 12.924 4 0.271 0.569 0.941 1.190 1.533 2.132 2.776 4 2.999 3.298 3.747 4.088 4.604 5.598 8.610 5 0.267 0.559 0.920 1.156 1.476 2.015 2.571 5 2.757 3.003 3.365 3.634 4.032 4.773 6.869 в 0.265 0.553 0.906 1.134 1.440 1.943 2.447 6 2.612 2.829 3.143 3.372 3.707 4.317 5.959 7 0.263 0.549 0.896 1.119 1.415 1.895 2.365 7 2.517 2.715 2.998 3.203 3.499 4.029 5.408 8 0.262 0.546 0.889 1.108 1.397 1.860 2.306 8 2.449 2.634 2.896 3.085 3.355 3.833 5.041 9 0.261 0.543 0.883 1.100 1.383 1.833 2.262 9 2.398 2.574 2.821 2.998 3.250 3.690 4.781 10 0.260 0.542 0.879 1.093 1.372 1.812 2.228 10 2.359 2.527 2.764 2.932 3.169 3.581 4.587 11 0.260 0.540 0.876 1.088 1.363 1.796 2.201 11 2.328 2.491 2.718 2.879 3.106 3.497 4.437 12 0.259 0.539 0.873 1.083 1.356 1.782 2.179 12 2.303 2.461 2.681 2.836 3.055 3.428 4.318 13 0.259 0.538 0.870 1.079 1.350 1.771 2.160 13 2.282 2.436 2.650 2.801 3.012 3.372 4.221 14 0.258 0.537 0.868 1.076 1.345 1.761 2.145 14 2.264 2.415 2.624 2.771 2.977 3.326 4.140 15 0.258 0.536 0.866 1.074 1.341 1.753 2.131 15 2.249 2.397 2.602 2.746 2.947 3.286 4.073 16 0.258 0.535 0.865 1.071 1.337 1.746 2.120 16 2.235 2.382 2.583 2.724 2.921 3.252 4.015 17 0.257 0.534 0.863 1.069 1.333 1.740 2.110 17 2.224 2.368 2.567 2.706 2.898 3.222 3.965 18 0.257 0.534 0.862 1.067 1.330 1.734 2.101 18 2.214 2.356 2.552 2.689 2.878 3.197 3.922 19 0.257 0.533 0.861 1.066 1.328 1.729 2.093 2.205 2.346 2.539 2.674 2.861 3.174 3.883 20 0.257 0.533 0.860 1.064 1.325 1.725 2.086 20 2.197 2.336 2.528 2.661 2.845 3.153 3.850 21 0.257 0.532 0.859 1.063 1.323 1.721 2.080 21 2.189 2.328 2.518 2.649 2.831 3.135 3.819 22 0.256 0.532 0.858 1.061 1.321 1.717 2.074 22 2.183 2.320 2.508 2.639 2.819 3.119 3.792 23 0.256 0.532 0.858 1.060 1.319 1.714 2.069 23 2.177 2.313 2.500 2.629 2.807 3.104 3.768 24 0.256 0.531 0.857 1.059 1.318 1.711 2.064 24 2.172 2.307 2.492 2.620 2.797 3.091 3.745 25 0.256 0.531 0.856 1.058 1.316 1.708 2.060 25 2.167 2.301 2.485 2.612 2.787 3.078 3.725 26 0.256 0.531 0.856 1.058 1.315 1.706 2.056 27 0.256 0.531 0.855 1.057 1.314 1.703 2.052 28 0.256 0.530 0.855 1.056 1.313 1.701 2.048 - 29 0.256 0.530 0.854 1.055 1.311 1.699 2.045 30 0.256 0.530 0.854 1.055 1.310 1.697 2.042 40 0.255 0.529 0.851 1.050 1.303 1.684 2.021 60 0.254 0.527 0.848 1.045 1.296 1.671 2.000 120 0.254 0.526 0.845 1.041 1.289 1.658 1.980 8" 0.253 0.524 0.842 1.036 1.282 1.645 1.960 e 0.40 0.30 0.20 0.15 0.10 - <> 120 888 988 26 2.162 2.296 2.479 2.605 2.779 3.067 3.707 27 2.158 2.291 2.473 2.598 2.771 3.057 3.689 28 2.154 2.286 2.467 2.592 2.763 3.047 3.674 2.150 2.282 2.462 2.586 2.756 3.038 3.660 30 2.147 2.278 2.457 2.581 2.750 3.030 3.646 40 2.123 2.250 2.423 2.542 2.704 2.971 3.551 60 2.099 2.223 2.390 2.504 2.660 2.915 3.460 2.076 2.196 2.358 2.468 2.617 2.860 3.373 2.054 2.170 2.326 2.432 2.576 2.807 3.290 0.05 0.025 0.02 0.015 0.01 0.0075 0.005 0.0025 0.0005 a A a C
Transcribed Image Text:Critical Values of the t-Distribution Critical Values of the t-Distribution a a 0.40 0.30 0.20 0.15 0.10 0.05 0.025 0.02 0.015 0.01 0.0075 0.005 0.0025 0.0005 1 0.325 0.727 1.376 1.963 3.078 6.314 12.706 1 15.894 21.205 31.821 42.433 63.656 127.321 636.578 2 0.289 0.617 1.061 1.386 1.886 2.920 4.303 2 4.849 5.643 6.965 8.073 9.925 14.089 31.600 3 0.277 0.584 0.978 1.250 1.638 2.353 3.182 3 3.482 3.896 4.541 5.047 5.841 7.453 12.924 4 0.271 0.569 0.941 1.190 1.533 2.132 2.776 4 2.999 3.298 3.747 4.088 4.604 5.598 8.610 5 0.267 0.559 0.920 1.156 1.476 2.015 2.571 5 2.757 3.003 3.365 3.634 4.032 4.773 6.869 в 0.265 0.553 0.906 1.134 1.440 1.943 2.447 6 2.612 2.829 3.143 3.372 3.707 4.317 5.959 7 0.263 0.549 0.896 1.119 1.415 1.895 2.365 7 2.517 2.715 2.998 3.203 3.499 4.029 5.408 8 0.262 0.546 0.889 1.108 1.397 1.860 2.306 8 2.449 2.634 2.896 3.085 3.355 3.833 5.041 9 0.261 0.543 0.883 1.100 1.383 1.833 2.262 9 2.398 2.574 2.821 2.998 3.250 3.690 4.781 10 0.260 0.542 0.879 1.093 1.372 1.812 2.228 10 2.359 2.527 2.764 2.932 3.169 3.581 4.587 11 0.260 0.540 0.876 1.088 1.363 1.796 2.201 11 2.328 2.491 2.718 2.879 3.106 3.497 4.437 12 0.259 0.539 0.873 1.083 1.356 1.782 2.179 12 2.303 2.461 2.681 2.836 3.055 3.428 4.318 13 0.259 0.538 0.870 1.079 1.350 1.771 2.160 13 2.282 2.436 2.650 2.801 3.012 3.372 4.221 14 0.258 0.537 0.868 1.076 1.345 1.761 2.145 14 2.264 2.415 2.624 2.771 2.977 3.326 4.140 15 0.258 0.536 0.866 1.074 1.341 1.753 2.131 15 2.249 2.397 2.602 2.746 2.947 3.286 4.073 16 0.258 0.535 0.865 1.071 1.337 1.746 2.120 16 2.235 2.382 2.583 2.724 2.921 3.252 4.015 17 0.257 0.534 0.863 1.069 1.333 1.740 2.110 17 2.224 2.368 2.567 2.706 2.898 3.222 3.965 18 0.257 0.534 0.862 1.067 1.330 1.734 2.101 18 2.214 2.356 2.552 2.689 2.878 3.197 3.922 19 0.257 0.533 0.861 1.066 1.328 1.729 2.093 2.205 2.346 2.539 2.674 2.861 3.174 3.883 20 0.257 0.533 0.860 1.064 1.325 1.725 2.086 20 2.197 2.336 2.528 2.661 2.845 3.153 3.850 21 0.257 0.532 0.859 1.063 1.323 1.721 2.080 21 2.189 2.328 2.518 2.649 2.831 3.135 3.819 22 0.256 0.532 0.858 1.061 1.321 1.717 2.074 22 2.183 2.320 2.508 2.639 2.819 3.119 3.792 23 0.256 0.532 0.858 1.060 1.319 1.714 2.069 23 2.177 2.313 2.500 2.629 2.807 3.104 3.768 24 0.256 0.531 0.857 1.059 1.318 1.711 2.064 24 2.172 2.307 2.492 2.620 2.797 3.091 3.745 25 0.256 0.531 0.856 1.058 1.316 1.708 2.060 25 2.167 2.301 2.485 2.612 2.787 3.078 3.725 26 0.256 0.531 0.856 1.058 1.315 1.706 2.056 27 0.256 0.531 0.855 1.057 1.314 1.703 2.052 28 0.256 0.530 0.855 1.056 1.313 1.701 2.048 - 29 0.256 0.530 0.854 1.055 1.311 1.699 2.045 30 0.256 0.530 0.854 1.055 1.310 1.697 2.042 40 0.255 0.529 0.851 1.050 1.303 1.684 2.021 60 0.254 0.527 0.848 1.045 1.296 1.671 2.000 120 0.254 0.526 0.845 1.041 1.289 1.658 1.980 8" 0.253 0.524 0.842 1.036 1.282 1.645 1.960 e 0.40 0.30 0.20 0.15 0.10 - <> 120 888 988 26 2.162 2.296 2.479 2.605 2.779 3.067 3.707 27 2.158 2.291 2.473 2.598 2.771 3.057 3.689 28 2.154 2.286 2.467 2.592 2.763 3.047 3.674 2.150 2.282 2.462 2.586 2.756 3.038 3.660 30 2.147 2.278 2.457 2.581 2.750 3.030 3.646 40 2.123 2.250 2.423 2.542 2.704 2.971 3.551 60 2.099 2.223 2.390 2.504 2.660 2.915 3.460 2.076 2.196 2.358 2.468 2.617 2.860 3.373 2.054 2.170 2.326 2.432 2.576 2.807 3.290 0.05 0.025 0.02 0.015 0.01 0.0075 0.005 0.0025 0.0005 a A a C
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