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Given a random sample of size 22 from a normal distribution, find k such that (a) P(-1.721

Given a random sample of size 22 from a normal distribution, find k such that (a) P(-1.721

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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I need help with this please parts a to c

Given a random sample of size 22 from a normal distribution, find k such that (a) P(-1.721 <T<k) = 0.945. (b) Find P(k<T<2.080) = 0.075. (c) Find P(-k<T<k) = 0.98. Click here to view page 1 of the table of critical values of the t-distribution. Click here to view page 2 of the table of critical values of the t-distribution. (a) k= (Round to three decimal places as needed.)
Transcribed Image Text:Given a random sample of size 22 from a normal distribution, find k such that (a) P(-1.721 <T<k) = 0.945. (b) Find P(k<T<2.080) = 0.075. (c) Find P(-k<T<k) = 0.98. Click here to view page 1 of the table of critical values of the t-distribution. Click here to view page 2 of the table of critical values of the t-distribution. (a) k= (Round to three decimal places as needed.)
Critical Values of the t-Distribution > > Critical Values of the t-Distribution a a せ 0.02 0.015 0.01 0.0075 0.005 0.0025 0.0005 0.40 0.30 0.20 0.15 0.10 0.05 0.025 1 15.894 21.205 31.821 42.433 63.656 127.321 636.578 1 0.325 0.727 1.376 1.963 3.078 6.314 12.706 2 4.849 5.643 6.965 8.073 9.925 2 14.089 31.600 0.289 0.617 1.061 1.386 1.886 2.920 4.303 3 3.482 3.896 4.541 3 0.277 0.584 0.978 1.250 5.047 5.841 7.453 1.638 12.924 2.353 3.182 4 2.999 3.298 3.747 4.088 4.604 5.598 4 0.271 0.569 0.941 1.190 8.610 1.533 2.132 2.776 5 2.757 3.003 5 0.267 3.365 3.634 4.032 0.559 0.920 4.773 6.869 1.156 1.476 2.015 2.571 6 2.612 2.829 3.143 3.372 3.707 4.317 в 0.265 0.553 0.906 5.959 1.134 1.440 1.943 2.447 7 0.263 0.549 0.896 1.119 1.415 1.895 2.365 8 0.262 0.546 0.889 1.108 1.397 1.860 2.306 9 0.261 0.543 0.883 1.100 1.383 1.833 2.262 10 0.260 0.542 0.879 1.093 1.372 1.812 2.228 11 0.260 0.540 0.876 1.088 1.363 1.796 2.201 12 0.259 0.539 0.873 1.083 1.356 1.782 2.179 13 0.259 0.538 0.870 1.079 1.350 1.771 2.160 14 0.258 0.537 0.868 1.076 1.345 1.761 2.145 15 15 0.258 0.536 0.866 1.074 1.341 1.753 2.131 16 0.258 0.535 0.865 1.071 1.337 1.746 2.120 17 0.257 0.534 0.863 1.069 1.333 1.740 2.110 27 28 40 60 120 22 88 881 18 0.257 0.534 0.862 1.067 1.330 1.734 2.101 19 0.257 0.533 0.861 1.066 1.328 1.729 2.093 20 0.257 0.533 0.860 1.064 1.325 1.725 2.086 21 0.257 0.532 0.859 1.063 1.323 1.721 2.080 22 0.256 0.532 0.858 1.061 1.321 1.717 2.074 23 0.256 0.532 0.858 1.060 1.319 1.714 2.069 24 0.256 0.531 0.857 1.059 1.318 1.711 2.064 25 25 0.256 0.531 0.856 1.058 1.316 1.708 2.060 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 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 0.255 0.529 0.851 1.050 1.303 1.684 2.021 0.254 0.527 0.848 1.045 1.296 1.671 2.000 0.254 0.526 0.845 1.041 1.289 1.658 1.980 0.253 0.524 0.842 1.036 1.282 1.645 1.960 0.40 0.30 0.20 0.15 0.10 0.05 0.025 a 'C'' e A - - › U 29 30 40 60 120 TRANNAN 88 P 7 2.517 2.715 2.998 3.203 3.499 4.029 5.408 8 2.449 2.634 2.896 3.085 3.355 3.833 5.041 9 2.398 2.574 2.821 2.998 3.250 3.690 4.781 10 2.359 2.527 2.764 2.932 3.169 3.581 4.587 11 2.328 2.491 2.718 2.879 3.106 3.497 4.437 12 2.303 2.461 2.681 2.836 3.055 3.428 4.318 13 2.282 2.436 2.650 2.801 3.012 3.372 4.221 14 2.264 2.415 2.624 2.771 2.977 3.326 4.140 2.249 2.397 2.602 2.746 2.947 3.286 4.073 16 2.235 2.382 2.583 2.724 2.921 3.252 4.015 17 2.224 2.368 2.567 2.706 2.898 3.222 3.965 18 2.214 2.356 2.552 2.689 2.878 3.197 3.922 19 2.205 2.346 2.539 2.674 2.861 3.174 3.883 20 2.197 2.336 2.528 2.661 2.845 3.153 3.850 21 2.189 2.328 2.518 2.649 2.831 3.135 3.819 22 2.183 2.320 2.508 2.639 2.819 3.119 3.792 23 2.177 2.313 2.500 2.629 2.807 3.104 3.768 24 2.172 2.307 2.492 2.620 2.797 3.091 3.745 2.167 2.301 2.485 2.612 2.787 3.078 3.725 26 2.162 2.296 2.479 2.605 2.779 3.067 3.707 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 2.147 2.278 2.457 2.581 2.750 3.030 3.646 2.123 2.250 2.423 2.542 2.704 2.971 3.551 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 0.02 0.015 0.01 0.0075 0.005 0.0025 0.0005 a
Transcribed Image Text:Critical Values of the t-Distribution > > Critical Values of the t-Distribution a a せ 0.02 0.015 0.01 0.0075 0.005 0.0025 0.0005 0.40 0.30 0.20 0.15 0.10 0.05 0.025 1 15.894 21.205 31.821 42.433 63.656 127.321 636.578 1 0.325 0.727 1.376 1.963 3.078 6.314 12.706 2 4.849 5.643 6.965 8.073 9.925 2 14.089 31.600 0.289 0.617 1.061 1.386 1.886 2.920 4.303 3 3.482 3.896 4.541 3 0.277 0.584 0.978 1.250 5.047 5.841 7.453 1.638 12.924 2.353 3.182 4 2.999 3.298 3.747 4.088 4.604 5.598 4 0.271 0.569 0.941 1.190 8.610 1.533 2.132 2.776 5 2.757 3.003 5 0.267 3.365 3.634 4.032 0.559 0.920 4.773 6.869 1.156 1.476 2.015 2.571 6 2.612 2.829 3.143 3.372 3.707 4.317 в 0.265 0.553 0.906 5.959 1.134 1.440 1.943 2.447 7 0.263 0.549 0.896 1.119 1.415 1.895 2.365 8 0.262 0.546 0.889 1.108 1.397 1.860 2.306 9 0.261 0.543 0.883 1.100 1.383 1.833 2.262 10 0.260 0.542 0.879 1.093 1.372 1.812 2.228 11 0.260 0.540 0.876 1.088 1.363 1.796 2.201 12 0.259 0.539 0.873 1.083 1.356 1.782 2.179 13 0.259 0.538 0.870 1.079 1.350 1.771 2.160 14 0.258 0.537 0.868 1.076 1.345 1.761 2.145 15 15 0.258 0.536 0.866 1.074 1.341 1.753 2.131 16 0.258 0.535 0.865 1.071 1.337 1.746 2.120 17 0.257 0.534 0.863 1.069 1.333 1.740 2.110 27 28 40 60 120 22 88 881 18 0.257 0.534 0.862 1.067 1.330 1.734 2.101 19 0.257 0.533 0.861 1.066 1.328 1.729 2.093 20 0.257 0.533 0.860 1.064 1.325 1.725 2.086 21 0.257 0.532 0.859 1.063 1.323 1.721 2.080 22 0.256 0.532 0.858 1.061 1.321 1.717 2.074 23 0.256 0.532 0.858 1.060 1.319 1.714 2.069 24 0.256 0.531 0.857 1.059 1.318 1.711 2.064 25 25 0.256 0.531 0.856 1.058 1.316 1.708 2.060 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 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 0.255 0.529 0.851 1.050 1.303 1.684 2.021 0.254 0.527 0.848 1.045 1.296 1.671 2.000 0.254 0.526 0.845 1.041 1.289 1.658 1.980 0.253 0.524 0.842 1.036 1.282 1.645 1.960 0.40 0.30 0.20 0.15 0.10 0.05 0.025 a 'C'' e A - - › U 29 30 40 60 120 TRANNAN 88 P 7 2.517 2.715 2.998 3.203 3.499 4.029 5.408 8 2.449 2.634 2.896 3.085 3.355 3.833 5.041 9 2.398 2.574 2.821 2.998 3.250 3.690 4.781 10 2.359 2.527 2.764 2.932 3.169 3.581 4.587 11 2.328 2.491 2.718 2.879 3.106 3.497 4.437 12 2.303 2.461 2.681 2.836 3.055 3.428 4.318 13 2.282 2.436 2.650 2.801 3.012 3.372 4.221 14 2.264 2.415 2.624 2.771 2.977 3.326 4.140 2.249 2.397 2.602 2.746 2.947 3.286 4.073 16 2.235 2.382 2.583 2.724 2.921 3.252 4.015 17 2.224 2.368 2.567 2.706 2.898 3.222 3.965 18 2.214 2.356 2.552 2.689 2.878 3.197 3.922 19 2.205 2.346 2.539 2.674 2.861 3.174 3.883 20 2.197 2.336 2.528 2.661 2.845 3.153 3.850 21 2.189 2.328 2.518 2.649 2.831 3.135 3.819 22 2.183 2.320 2.508 2.639 2.819 3.119 3.792 23 2.177 2.313 2.500 2.629 2.807 3.104 3.768 24 2.172 2.307 2.492 2.620 2.797 3.091 3.745 2.167 2.301 2.485 2.612 2.787 3.078 3.725 26 2.162 2.296 2.479 2.605 2.779 3.067 3.707 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 2.147 2.278 2.457 2.581 2.750 3.030 3.646 2.123 2.250 2.423 2.542 2.704 2.971 3.551 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 0.02 0.015 0.01 0.0075 0.005 0.0025 0.0005 a
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