Appendix Tables A-9 Table A.5 Critical Values for t Distributions 4, density curve Shaded area - a 0 .10 .05 025 .01 .005 .001 .0005 3.078 6.314 12.706 31.821 63.657 318.31 636.62 1.886 2.920 4.303 6.965 9.925 22.326 31.598 1.638 2.353 3.182 4.541 5.841 Jan AWN 1.533 10.213 12.924 2.132 2.776 3.747 4.604 7.173 8.610 1.476 2.015 2.571 3.365 4.032 5.893 6.869 1.440 1.943 2.447 3.143 3.707 5.208 5.959 1.415 1.895 2.365 2.998 3.499 4.785 5.408 1.397 1.860 2.306 2.896 3.355 4.501 5.041 1.383 1.833 2.262 2.821 3.250 4.297 .781 1.372 1.812 2.228 2.764 3.169 4.144 1.363 4.587 11 1.796 2.201 2.718 3.106 4.025 4.437 1.356 1.782 2.179 2.681 3.055 1.350 3.930 4.318 1.771 2.160 2.650 3.012 1.345 3.852 1.761 2.145 4.221 2.624 2.977 3.787 4.140 1.341 1.753 2.131 2.602 2.947 3.733 1.337 1.746 4.073 2.120 2.583 2.921 3.686 4.015 1.333 1.740 2.1 10 2.567 2.898 3.646 3.965 1.330 1.734 2.101 2.552 2.878 3.610 1.328 3.922 1.729 2.093 2.539 2.861 3.579 3.883 1.325 1.725 2.086 2.528 2.845 3.552 1.323 3.850 1.721 2.080 2.518 2.831 1.321 3.527 1.717 3.819 2.074 2.508 2.819 3.505 1.319 1.714 3.792 2.069 2.500 2.807 3.485 3.767 1.318 1.711 2.064 2.492 2.797 3.467 3.745 1.316 1.708 2.060 2.485 2.787 3.450 3.725 1.315 1.706 2.056 2.479 2.779 3.435 3.707 1.314 1.703 2.052 2.473 2.771 3.421 1.313 3.690 1.701 2.048 2.467 2.763 1.311 3.408 3.674 1.699 2.045 2.462 2.756 3.396 3.659 30 1.310 1.697 2.042 2.457 2.750 32 3.385 1.309 3.646 1.694 2.037 2.449 2.738 3.365 34 1.307 3.622 1.691 2.032 2.441 2.728 3.348 36 3.601 1.306 1.688 2.028 2.434 2.719 3.333 38 3.582 1.304 1.686 2.024 2.429 2.712 3.319 3.566 40 1.303 1.684 2.021 2.423 2.704 3.307 3.551 50 1.299 1.676 2.009 2.403 60 2.678 3.262 1.296 3.496 1.671 2.000 2.390 120 2.660 3.232 1.289 3.460 1.658 1.980 2.358 2.617 3.160 3.373 1.282 1.645 1.960 2.326 2.576 3.090 3.291A-6 Appendix Tables Table A.3 Standard Normal Curve Areas D(2) = P(Z s z) Standard normal density curve Shaded area = (z) 0 Z .00 .01 .02 .03 .04 .05 .06 .07 .08 09 -3.4 0003 0003 0003 .0003 0003 0003 .0003 .0003 0003 0002 -3.3 .0005 .0005 0005 .0004 0004 0004 0004 0004 0004 0003 -3.2 .0007 0007 0006 .0006 0006 .0006 0006 0005 0005 0005 -3.1 .0010 0009 0009 .0009 0008 0008 0008 0008 0007 0007 -3.0 .0013 .0013 .0013 .0012 .0012 .001 1 .0011 .0011 .0010 0010 -2.9 .0019 .0018 0017 .0017 0016 0016 .0015 .0015 .0014 0014 -2.8 .0026 0025 .0024 .0023 .0023 .0022 0021 .0021 .0020 0019 -2.7 0035 .0034 0033 .0032 0031 0030 .0029 0028 .0027 .0026 -2.6 0047 .0045 .0044 .0043 .0041 .0040 0039 .0038 0037 0036 -2.5 .0062 .0060 0059 0057 .0055 0054 0052 0051 0049 0038 -2.4 .0082 .0080 .0078 .0075 .0073 .0071 .0069 .0068 .0066 .0064 -2.3 .0107 .0104 .0102 .0099 .0096 .0094 .0091 .0089 .0087 .0084 -2.2 .0139 .0136 .0132 .0129 .0125 .0122 .01 19 .0116 .0113 .01 10 -2.1 .0179 .0174 .0170 .0166 .0162 .0158 .0154 .0150 .0146 .0143 -2.0 .0228 .0222 .0217 .0212 .0207 .0202 .0197 .0192 .0188 .0183 -1.9 .0287 .0281 .0274 .0268 .0262 .0256 .0250 .0244 .0239 .0233 -1.8 .0359 .0352 .0344 .0336 0329 .0322 .0314 .0307 .0301 0294 -1.7 .0446 .0436 .0427 .0418 .0409 .0401 0392 .0384 .0375 0367 -1.6 .0548 0537 .0526 .0516 0505 0495 .0485 .0475 0465 0455 -1.5 .0668 .0655 .0643 .0630 .0618 .0606 .0594 .0582 .0571 0559 -1.4 0808 0793 0778 0764 0749 0735 0722 0708 .0694 0681 .0968 .0951 .0934 .0918 .0901 .0885 .0869 0853 0838 0823 -1.2 .1151 .1131 .1112 .1093 .1075 1056 .1038 .1020 .1003 0985 -1.1 .1357 .1335 .1314 . 1292 .1271 1251 .1230 .1210 .1 190 .1170 -1.0 .1587 1562 .1539 .1515 .1492 1469 .1446 .1423 .1401 .1379 -0.9 .1841 .1814 .1788 1762 1736 .1711 . 1685 .1660 .1635 1611 -0.8 .21 19 .2090 .2061 .2033 .2005 .1977 . 1949 .1922 .1894 .1867 -0.7 .2420 .2389 .2358 .2327 .2296 .2266 .2236 .2206 .2177 .2148 -0.6 .2743 .2709 .2676 .2643 .2611 .2578 .2546 .2514 .2483 .2451 -0.5 .3085 .3050 .3015 .2981 2946 .2912 .2877 .2843 .2810 .2776 -0.4 3446 .3409 .3372 .3336 3300 .3264 .3228 .3192 .3156 .3121 -0.3 .3821 .3783 .3745 .3707 3669 .3632 .3594 .3557 .3520 .3482 -0.2 4207 4168 4129 4090 4052 4013 .3974 3936 .3897 .3859 -0.1 4602 4562 4522 4483 4443 4404 4364 .4325 4286 4247 -0.0 .5000 .4960 4920 .4880 4840 .4801 .4761 4721 .4681 .4641\fThe life times, Y in years of a certain brand of low-grade lightbulbs follow an exponential distribution with a mean of 0.8 years. A tester makes random observations of the life times of this particular brand of lightbulbs and records them one by one as either a success if the life time exceeds 1 year, or as a failure otherwise. (a) Find the probability that the rst success occurs in the fth ob- servation. (b) Find the probability of the third success occurring after the fourth observation