Question

1. The life time of a certain brand of bulbs produced by a company is normally distributed, with mean 210 hours and standard deviation 56 hours. What is the probability that a bulb picked at random from this company’s products will have a life time of:

(i) at least 300 hours,

(ii) at most 100 hours,

(iii) between 150 and 250 hours.

Answer 1

L 0.06 0 50000 0.09 53586 +1 +0.1 +0.2 +0.3 +0.4 +0.5 (0.01 50 54380 58317 62172 1.65910 1.69497 157535 1.61409 65173 168793 (+0.7) 176115) Sub 72240 175490 178524 181327 183891 186214 .88298 +0.9 +1 +1.1 +1.2 +1.3 .81859 1.84375 1.86650 .88686 190490 192073 +1.4 +1.6 53983 57926 161791 165542 1.69146 172575 175804 178814 181594 .84134 186433 188493 190320 191924 1.93319 194520 195543 196407 197128 197725 198214 198610 198928 99180 199379 199534 199653 199744 199813 199865 199903 199931 199952 +1.8 +1.9 +2 +2.1 +2.2 +2.3 +2.4 +2.5 +2.6 +2.7 +2.8 +2.9 +3 +3.1 +3.2 +3.3 +3.4 +3.5 +3.6 +3.7 +3.8 +3.9 +4 194630 95567 196485 197193 197778 198257 198645 198956 199202 199396 199547 199664 199752 199819 199869 199906 199934 99953 199968 199978 199985 199990 1.99993 199995 199997 0.02 150798 154776 158706 1.62552 466276 .69847 173237 1.76424 1.79389 182121 184614 186864 188877 190658 92220 193574 194738 195728 196562 197257 197831 198300 198679 198983 199224 199413 199560 1.99674 199760 199825 199874 1.99910 199936 199955 199969 199978 199985 199990 1.99993 199996 199997 0.03 51197 155172 1.59095 162930 166640 170194 173565 76730 179673 182381 184849 .87076 189065 190824 192364 193699 1.94845 195818 196638 197320 1.97882 198341 198713 199010 199245 199430 .99573 199683 199767 199831 199878 199913 199938 199957 199970 199979 199986 199990 1.99994 199996 199997 0.04 51595 55567 159483 .63307 .67003 170540 .73891 177035 479955 .82639 1.85083 187286 1.89251 190988 92507 93822 194950 195907 1.96712 197381 197932 198382 198745 199036 199266 199446 199585 199693 199774 199836 199882 199916 199940 99958 199971 199980 199986 199991 1.99994 199996 199997 0.05 51994 155966 159871 163683 .67364 170884 74215 77337 1.80234 182894 185314 187493 189435 91149 192647 1.93943 1.95053 1.95994 196784 197441 97982 198427 198778 199061 1.99286 199461 199598 1.99702 199781 199841 1.99886 199918 199942 199960 1.99972 199981 199987 199991 199994 199996 52392 156360 .60257 164058 167724 71226 74537 77637 1.80511 183147 185543 .87698 189617 91308 192785 194062 195154 196080 196856 197500 198030 198461 198809 199086 199305 199477 199609 199711 199788 199846 199889 199921 99944 199961 199973 199981 199987 199992 199994 199996 199998 0.07 52790 156749 .60642 .54431 1.68082 171566 174857 77935 .80785 183398 185769 187900 1.89796 191466 92922 194179 195254 196164 96926 197558 198077 198500 198840 199111 199324 199492 1.99621 199720 199795 199851 199893 199924 199946 199962 199974 199982 99988 199992 1.99995 199996 0.08 153188 157142 1.61026 .64803 168439 171904 175175 178230 .81057 183646 1.85993 .88100 189973 91621 193056 194295 195352 196246 196995 197615 1.98124 198537 198870 199134 199343 199506 199632 199728 199801 199856 199896 1.99926 199948 99964 199975 199983 199988 199992 1.99995 199997 99998 190147 91774 193189 194408 195449 196327 97062 197670 198169 198574 198899 199158 199361 199520 199643 199736 199807 99861 199900 199929 199950 199965 199976 199983 199989 199992 199995 199997 199998 199966 199977 199984 199989 199993 199995 199997 199997 99998

Z 0 0.06 0.07 0.08 0.09 0.05 48006 44034 46812 -0 -0.1 -0.2 -0.3 -0.4 -0.5 -0.6 -0.7 -0.8 50000 46017 42074 38209 .34458 130854 127425 124196 43640 39743 35942 132276 128774 25463 22363 43251 1.39358 35569 31918 28434 25143 22065 19215 42858 38974 135197 131561 128096 24825 121770 18943 11634 114007 46414 42465 138591 34827 31207 127760 124510 21476 118673 121186 .18406 15866 13567 16109 13786 14231 19489 16853 11457 12302 10383 .08692 07215 IZTU 11702 09853 10204 -1 一 -1.2 -1.3 -1.4 -1.5 -1.6 -1.7 11900 10027 .08379 106944 105705 08226 1.06811 105592 104648 03754 .04551 103673 02938 -1.9 11507 09680 108076 106681 105480 104457 .03593 .02872 102275 201786 201390 .01072 400820 200621 200466 100347 0.01 49601 45620 41683 37828 134090 30503 27093 23885 .20897 .18141 15625 13350 11314 09510 .07927 1.06552 105370 104363 03515 02807 202222 .01743 201355 .01044 1.00798 200604 .00453 200336 1.00248 .00181 400131 .00094 00066 .00047 200032 200022 400015 200010 .00007 .00005 .00003 0.02 49202 45224 41294 137448 133724 130153 126763 123576 120611 .17879 15386 13136 111123 109342 .07780 1.06426 .05262 104272 103438 102743 .02169 201700 201321 201017 00776 200587 200440 200326 200240 400175 .00126 100090 200064 400045 400031 400022 200015 200010 200007 100004 400003 0.03 48803 44828 140905 37070 133360 129806 26435 123270 120327 17619 15151 12924 10935 109176 .07636 1.06301 105155 104182 .03362 02680 102118 201659 287 .00990 200755 .00570 .00427 200317 200233 200169 1.00122 200087 .00062 400043 400030 1.00021 1.00014 1.00010 200006 .00004 .00003 0.04 48405 44433 40517 36693 32997 129460 126109 21965 120045 17361 .14917 12714 110749 209012 107493 1.06178 105050 .04093 .03288 202619 102068 .01618 201255 200964 400734 200554 200415 200307 200226 .00164 1.00118 200084 .00060 200042 400029 200020 400014 100009 .00006 200004 200003 40129 36317 132636 129116 25785 22663 19766 117106 14686 12507 10565 108851 107353 106057 .04947 104006 103216 102559 102018 201578 201222 200939 200714 200539 200402 .00298 400219 .00159 200114 200082 200058 400040 100028 400019 200013 200009 100006 1.00004 400003 105938 .04846 103920 AP14 02500 Longyu 201539 201191 102330 201831 201426 201101 200914 200842 200639 200480 -2.1 -2.2 -2.3 -2.4 -2.5 -2.6 -2.7 -2.8 -2.9 -3 -3.1 -3.2 -3.3 -3.4 -3.5 -3.6 -3.7 -3.8 -3.9 -4 400357 200264 08534 07078 205821 4.04746 103836 1.03074 102442 .01923 201500 01160 .00889 .00676 .00508 200379 00280 .00205 200149 200107 200076 .00054 100038 .00026 .00018 .00012 200008 400005 1.00004 .00002 .00256 100187 .00695 200523 200391 200289 200212 200154 10011 200079 1.00056 .00039 100027 100019 1.00013 100008 400006 400004 100002 103005 02385 201876 201463 201130 .00866 400657 200494 200368 .00272 400199 200144 400104 200074 200052 400036 .00025 200017 200012 1.00008 400005 400003 100002 .00 135 100097 .00069 200193 400139 400100 .00071 100050 400035 100024 400017 100011 .00048 400034 100023 400016 100011 400007 100005 100003 100008 100005 100003 .00002