Math Statistic Formula Sheet

NEGATIVE z Scores .. z .00 .05 ·---- -- .06 .03 ,02 .04 --- -·---- --- - - •• ·-·- .01 -- 'ifni:i" .cicio1 ,0003 .0005 ,0007 .0010 .0013 .0019 .0026 :0035 ,0047 ,0062 .0082 ,0107 ,0139 ,0179 ,0228 ,0287 .0359 lo'w�-, -3.4 -3.3 -3.2 -3.1 -3,0 -2,9·· -2.8 .-2:7 -2,6 -2.5 -2.4 -2.3 -2.2 -2.1 -2.0 -1,9 -1.8 -1,7 -1.6 -1.5 .0446 -1.4 -1,3 -1.2 -1.0 -0.9 -0.8 -0;1 -0.6 -0.5 -0.4 �o.3· -0.2 -0.1 -o.o .. .0548 ,0668 .0808 ,0968 ,1151 .1357 .1587 .1841, .1335 ,1562 .0003 .0005 .0006 ,0009 .0013 ,0018 .0024 ·,0033 .0044 .0059 .0078 .0102 .0132 .0170 .0217 ,0274 .0344 .0427 .0526 .0003 .0004 .0006 .0009 .0012 .0017 .0023 .0032 .0043 .0057 .0075 .0099 .0129 .0166 ,0212 .0268 .0336 .0418 .0516 ,0643 .0778 .0630 ,0764 ,1112 .1314 .1093 .1292 ,0934 .0918 .0003 .0004 .0006 .0008 ,0011 .0016 .0022 ,0030 .0040 .0054 .0071 .0094 .0003 ,0004 .0006 .coos .0012 ,0016 .0023 .0031 .0041 ,0055 .0073 ,0096 .0125 .0162 .0207 ,0262 .0329 .0409 .0505 .0618 .0749 .0901 ,1075 ,1271 .1492 ,1736 .2005 .2296 .2611 ,2946 .3300 ,3669 .0122 . .0158 .0202 ,0256 .0322 .0401 .0495 .0606 .0735 .0885 ,1056 ,1251 .1469 ,1711 .1977 .2266 .0003 .0004 .0006 .0008 .0011 .0015 .0021 ,0029 .0039 ,0052 .0069 .0091 .0119 ,0154 .0197 ,0250 .0314 ,0392 .0485 ,0594 .0721 .0869 .1038 ,1230 .1446 :0003 ,0004 .coos ,0008 .0011 ..0015 .0021 :0020 .0038 .0051 .0068 .0089 ,0116 .0150 ,0192 .0244 ,0307 .0384 .0475 .0582 .0708 .0853 .1020 . .1210: .. .0838 .1003 ·,c.i1iio ,3783 ,3745 ,4602 .4562 .4522 .4483 .4052 .4443 .4404 .4364 .4325 ,3936 .4286 ·,3483. ,3859 .4247 ,4960 ,4920 ,4880 .4840 .4801 .4761 .4721 ,4681 .4641 .4207 .sooo .2389 ,2709 .3050 ,3409 .4168 .1539 .1788 .2061 .2358 .2676 ,3015 ,3372 .4129 .1515 .1762 .2033 .2327 ,2643 .2981 ,3336 ,3707 .4090 .1685 .1949 ,1423 .1660 .1922 .2236 ,2206 .3632 .3228 .3594 .3567 .2578 .2912 .3264 .4013 .2546 .2877 .3974 ,2514 ,2843 .3192 0.0500 0.00S0 ·------� ·-------··--·· ---·- .. I ,1379 .1611 ,1867 .2148 .24S1 .2776 .3121 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 ,0823 .0985 •. :jj7ci ,3085 .3446 ,,3821 .1814 .2090 � � -2,575 . .0002 ,0003 ,0003 .0004 .coos ,0005 ,0007 .0007 .0010 ,0010 ,0,014 • il.OQl,4,-,. .: .0020 .0019 ;0027 :0026· .0037 .0036 .0049 ,0048 .0066 .0064 .0087 .0084 .0113 ,0110 ,0146 .0143 ,0188 ,0183 .0233 ,0239 .0301 ,0294 .0367 ,0375 .0465 .0455 .0559 .0571 ,0694 ,0681 .1401 ;1635 .1894 .2177 ,2483 ,2810 .3156 . 1, .3520 ' ,3897 ,2119 ,2420 .2743 NOTE.· For values of z below -3.49, use 0,0001 for the area. •use these common values that result from Interpolation: -1.64S .: z .0003 .0005 .0007 .0009 .0013 .0018 .0025 .0034 ,0045 .0060 .0080 ,0104 .0136 ,0174 ,0222 ,0281 .0351 .0436 .0537 ,0655 .0793 ,0951 .1131 POSi-TIVE z z Scores .09 .OB .07 ··-·- -- . ----- -3.50 -:-i,1 0 Standard Normal (z) Distribution: Cumulative Area from the LEFT ! ; 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2,9 3.0 3.1 3.2 3.3 3.4 3.50 and up (continued) Cumulative Area from the LEFT, .00 .5000 .5398 .5793 .6179 .6554 .6915 .7257 .7580 .7881 .8159 .8413 .8643 .8849 .9032 .9192 .9332 .9452 .9554 .9641 .9713 .9772 .9821 .9861 .9893 .9918 ,9938 .9953 .9965 .9974 ,9981 .9987 .9990 .9993 .9995 .9997 .9999 .01 .5040 .5438 .5832 ,6217 .6591 .6950 .7291 .7611 .7910 .8186 .8438 .8665 .8869 .9049 .9207 .9345 .9463 ,9564 .9649 .9719 .9778 .9826 .9864 .9896 .9920 .9940 .9955 .9966 .9975 .9982 .9987 .9991 .9993 .9995 .9997 .02 .5080 .5478 .5871 .6255 .6628 ,6985 .7324 ,7642 ,7939 ,8212 .8461 .8686 ,8888 ,9066 .9222 .9357 .9474 .9573 ,9656 .9726 .9783 ,9830 .9868 .9898 .9922 ,9941 .9956 .9967 .9976 .9982 .9987 .9991 .9994 .9995 .9997 .03 .5120 .5517 .5910 .6293 .6664 .7019 .7357 .7673 .7967 .8238 .8485 .8708 .8907 .9082 .9236 .9370 .9484 .9582 .9664 .9732 .9788 .9834 .9871 .9901 .9925 .9943 .9957 ,9968 .9977 .9983 ,9988 .9991 .9994 .9996 .9997 .OS .04 .5160 .5557 .5948 .6331 .6700 .7054 .7389 .7704 .7995 .8264 .8508 .8729 .8925 .9099 .9251 .9382 .9495 .9591 .9671 .9738 .9793 .9838 .9875 .9904 .9927 .9945 .9959 .9969 .9977 .9984 .9988 .9992 .9994 ,9996 .9997 NOTE: For values of z above 3.49, use 0.9999 for the area. •use these common values that result from interpolation: � Area 1.645 0.9500 2.575 0.9950 . .5199 .5596 .5987 .6368 .6736 .7088 .7422 .7734 .8023 .8289 .8531 .8749 .8944 .9115 .9265 .9394 .9505 .9599 .9678 .9744 .9798 .9842 .9878 .9906 .9929 .9946 .9960 .9970 .9978 .9984 .9989 .9992 .9994 .9996 .9997 .06 .5239 .5636 .6026 .6406 .6772 .7123 .7454 .7764 .8051 .8315 .8554 .8770 .8962 .9131 .9279 .9406 .9515 ,9608 .9686 .9750 .9803 .9846 .9881 .9909 .9931 .9948 .9961 .9971 .9979 .9985 .9989 .9992 .9994 .9996 .9997 .OB .07 .5279 .5675 .6064 .6443 .6808 • ..7157 .7486 .7794 .8078 .8340 .8577 .8790 .8980 .9147 .9292 .9418 .9525 .9616 .9693 .9756 .9808 .9850 .9884 .9911 .9932 .9949 .9962 .9972 .9979 .9985 .9989 .9992 .9995 .9996 .9997 . .5319 .5714 .6103 .6480 .6844 .7190 .7517 .7823 .8106 .8365 .8599 .8810 .8997 .9162 .9306 .9429 .9535 .9625 .9699 .9761 .9812 .9854 .9887 .9913 .9934 .9951 .9963 .9973 .9980 .9986 .9990 .9993 .9995 .9996 .9997 ,09 .5359 .5753 .6141 .6517 .6879 .7224 .7549 .7852 .8133 .8389 .8621 .8830 .9015 .9177 .9319 .9441 .9545 .9633 .9706 .9767 .9817 .9857 .9890 .9916 .9936 .9952 .9964 .9974 .9981 .9986 .9990 .9993 .9995 .9997 .9998 Common Critical Values Confidence Critlcal Level Value 0.90 1.645 0.95 1.96 0.99 2.575 0