Suppose that the measured voltage in a certain electric circuit has a normal distribution with mean 125 and standard deviation 3. If 3 independent measurements of the voltage are made, what is the possibility that all three measurements will lie between 120 and 128?Define Degrees of Freedom and Type-Two error. The average score of a sixth-grader in a certain school district on a math aptitude exam is 10 89 with a standard deviation of, 6.4. A random sample of 28 students in one school was taken. The mean score of these students was 84. Does this indicate that the students of this school are significantly slower in their mathematical ability? Use 5% Level of significance. (Necessary chart 1 is attached below).Appendix A Statutical Tables and Proofs Table A.4 (continued) Critical Values of the t. Distribution a 0.02 0.015 0.01 0.0075 0.005 0.0025 0.0005 15.894 21.205 31.821 12.433 63.056 127.321 4.849 5.643 538.576 6.965 8.073 9.925 14.089 31.600 3.482 3.89 4.541 5.047 5.84 7.453 12.924 2.989 J.29 3.747 4.088 4.004 5.598 8.610 2.757 3.003 3.365 3.634 4.032 4.773 6.809 2.612 2.829 3.143 3.372 J.707 4.317 5.959 2.517 2.715 2.996 J.200 3.499 4.029 5.408 2.449 2.834 2.896 3.085 3.355 3.833 5.041 2.398 2.574 2.821 2.998 3.250 3.890 4.781 10 2.359 2.527 2.764 2.912 3.169 3.581 4.587 11 2.328 2.491 2.718 2.879 3.106 3.497 1.437 12 2.303 2.401 2.681 2.836 3.055 3.428 4.318 13 2.282 2.436 2.650 2.301 3.012 3.372 1.221 14 2.284 2.415 2.624 2. 171 2.97 3.32 1.140 15 2.249 2.397 2.602 2.746 2.947 3.280 4.073 2.235 2.382 2.583 2.721 2.921 3.252 1015 17 2.224 2.308 2.587 2. 706 2.898 3.222 3.905 18 2.214 2.356 2.552 2.859 2.878 3.197 3972 19 2.205 2.340 2.539 2.674 2.861 3.174 3.883 20 2.197 2.336 2.528 2.081 2.845 3.153 3.850 21 2.189 2.328 2.518 2.849 2.831 3.135 3.819 22 2.183 2.320 2.508 2.839 2.819 3.119 3.792 23 2.177 2.313 2.500 2.829 2.807 3.104 3.768 24 2.172 2.307 2.492 2.620 2.797 3.091 3.745 25 2.107 2.301 2.485 2.012 2.787 3.078 3.725 26 2.162 2.29 2.479 2.005 2.779 3.087 3.707 27 2.158 2.291 2.473 2.396 2.771 3.057 3.689 28 2.154 2.236 2.467 2. 382 2.783 3.047 3.074 29 2.150 2.282 2.462 2.586 2.756 3.038 3.060 2.750 3.848 30 2.147 2.278 2.457 2.581 3.030 2.542 2.704 2.971 1.551 40 2.123 2.250 2.423 2.504 2.080 2.915 3.400 CO 2.099 2.223 2.390 2.017 2.860 3.373 2.468 3.290 120 2.076 2.196 2.358 2.576 2.807 2432 2.054 2.170 2.328R Student t. Distribution Probability Table Table A.4 Critical Values of the t-Distribution 0.40 0.30 0.20 0.15 0.10 0.05 0.025 0.325 0.727 1.376 1.963 3.078 6.314 12.706 0.289 0.617 1.061 1.386 1.886 2.920 4.303 0.277 0.584 0.978 1.250 1.638 2.353 3.182 0.271 0.569 0.941 1.190 1.533 2.132 2.776 0.267 0.559 0.920 1.156 1.476 2.015 2.571 0.265 0.553 0.906 1.134 1.440 1.943 2.447 0.263 0.549 0.896 1.119 1.415 1.895 2.365 0.262 0.546 0.889 1.108 1.397 1.860 2.306 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 12 2.201 0.259 0.539 0.873 1.083 1.356 1.782 13 2.179 0.259 0.538 0.870 1.079 1.350 1.771 14 2.160 0.258 0.537 0.868 1.076 1.345 1.761 15 2.145 0.258 0.536 0.866 1.074 1.341 1.753 2.131 16 0.258 0.535 0.865 1.071 17 1.337 1.746 0.257 0.534 2.120 0.863 1.069 18 1.333 1.740 0.257 2.110 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 20 0.257 2.093 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 22 2.080 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 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 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 0.253 0.524 0.842 1.036 1.282 1.645 1.960