Question

Solve the problem. Round three decimal places as needed. Intelligence Quotient (IQ) scores are normally distributed with a mean of 100 and a standard deviation of 15. If 9 people are randcomly selected, what is the probability they will have a mean IQ score between 105 and 110?(round three decimal places)

Answer 1

I am attaching the normal table P(Z>z).

TABLE III. THE NORMAL PROBABILITY INTEGRAL O I 2 3 4 5 6 8 9 o o'o OI 02 03 0.4 50000 49601 49202 48803 48405 46017 45620 45224 44828 44433 42074 41683 41294 40905 40517 38209 37828 37448 37070 36693 34458 34090 33724 33360 32997 48006 47608 47210 46812 46414 44038 4364443251 42858 42465 40129 39743 39358 38974 38591 36317 35942 35569 35197 34827 32636 32276 31918 31561 31207 0.5 0.6 07 0.8 0:9 30854 30503 30153 29806 29460 27425 27093 26763 26435 26109 24196 23885 23576 23270 22965 21186 20897 20611 20327 20045 18406 18141 17879 17619 17361 29116 28774 2843428096 29760 25785 25463 25143 24825 24510 22663 22363 22065 . 21770 21476 19766 19489 19215 18943 18673 17106 16853 16602 16354 16109 I'O I'I I 2 I'3 I'4 15866 15625 15386 15151 14917 13567 13350 13136 12924 12714 11507 I1314 III23 10935 10749 o'o 96800 95098 93418 91759 90123 80757 79270 77804 76359 74934 14686 14457 14231 14007 13786 I 2507 12302 I2100 11900 11702 10565 10383 10204 10027 98525 88508 86915 85343 83793 82264 73529 72145 70781 69437 68112 I'5 1.6 I 7 1.8 19 66807 65522 64255 63008 61780 54799 53699 52616 51551 50503 44565 43633 42716 41815 40930 35930 35148 34380 33625 32884 28717 28067 27429 26803 26190 60571 59380 58208 57053 55917 49471 48457 47460 46479 45514 40059 39204 38364 37538 36727 32157 31443 30742 30054 29379 25588 24998 24419 23852 23295 20 21 22 23 2'4 22750 22216 21692 21178 20675 17864 17429 17003 16586 16177 13903 13553 13209 12874 12545 10724 10444 10170 99031 96419 0:04 81975 79763 77603 75494 73436 20182 19699 192 26 18763 18309 15778 15386 15003 14629 14262 12224 11911 11604 11304 IIOII 93867 91375 88940 86563 84242 71428 69469 67557 65691 63872 25 2.6 27 2.8 29 62097 60366 58677 57031 55426 46612 45271 43965 42692 41453 34670 33642 32641 31667 30720 25551 24771 24012 23274 22557 18658 18071 17502 16948 16411 53861 52336 50849 49400 47988 40246 39070 37926 36811 35726 29798 28901 28028 27179 26354 21860 21182 20524 19884 19262 15889 15382 14890 14412 13949 11442 11067 10703 10350 10008 81635 78885 76219 73638 71136 57703 55706 53774 51904 50094 40406 38971 37584 36243 34946 28029 2700926023 25071 24151 30 31 32 3:3 34 3.5 306 37 3.8 13499 13062 1 2639 12228 11829 0:08 96760 93544 90426 87403 84474 68714 66367 64095 61895 59765 48342 46648 45009 43423 41889 33693 32481 31311 30179 29086 23263 22405 21577 20778 20006 15911 15310 1473014171 13632 10780 10363 99611 95740 92010 0.04 72348 69483 66726 64072 61517 48096 46148 44274 42473 40741 31671 30359 29099 27888 26726 20658 19783 18944 18138 17365 13346 12769 12215 11685 11176 0.085399 81627 78015 74555 71241 54125 51685 49350 47117 44979 19262 18543 178 17180 16534 13112 12611 I2I28 11662 II213 88417 84957 81624 78414 75324 59059 56694 54418 52228 50122 39076 37475 35936 34458 33037 3.9 40 41 42 43 44 25609 24536 23507 22518 21569 16624 15912 1523014575 13948 10689 10221 97736 93447 89337 68069 65031 62123 59340 56675 42935 40980 39110 37322 35612 45 4.6 4.7 4.8 33977 32414 30920 29492 28127 21125 20133 19187 18283 17420 13008 12386 11792 I1226 10686 0.06 79333 75465 71779 68267 64920 47918 45538 43272 41115 39061 26823 25577 24386 23249 22162 16597 15810 15060 14344 13660 10171 96796 92113 87648 83391 61731 58693 55799 53043 50418 37107 35247 33476 31792 30190 49

If XN+/100, 15² Nf 10, 11 the XNl 100 P(los < X <110) PL 105-100 LZ< llo-loo 1513 110-120] 1513 2 =PLIS 2 La PORODOS p(221) - P(272) 0.022750 0.15866 = 0.13591 = 0.136