Exam (elaborations)
TESTBANK FOR UNDERSTANDING BASIC STATISTICS 6th EDITION
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TESTBANK FOR UNDERSTANDING BASIC STATISTICS 6th EDITION
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,, Areas of a Standard Normal Distribution
(a) Table of Areas to the Left of z
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
z 0 ⫺3.1 .0010 .0009 .0009 .0009 .0008 .0008 .0008 .0008 .0007 .0007
⫺3.0 .0013 .0013 .0013 .0012 .0012 .0011 .0011 .0011 .0010 .0010
Table entry for z is the area to the left ⫺2.9 .0019 .0018 .0018 .0017 .0016 .0016 .0015 .0015 .0014 .0014
of z. ⫺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 .0048
⫺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 .0119 .0116 .0113 .0110
⫺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 .0351 .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 .0721 .0708 .0694 .0681
⫺1.3 .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 .1190 .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 .2119 .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 .3483
⫺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
For values of z less than 23.49, use 0.000 to approximate the area.
, Areas of a Standard Normal Distribution continued
z .00 .01 .02 .03 .04 .05 .06 .07 .08 .09
0.0 .5000 .5040 .5080 .5120 .5160 .5199 .5239 .5279 .5319 .5359
0.1 .5398 .5438 .5478 .5517 .5557 .5596 .5636 .5675 .5714 .5753
0.2 .5793 .5832 .5871 .5910 .5948 .5987 .6026 .6064 .6103 .6141
0.3 .6179 .6217 .6255 .6293 .6331 .6368 .6406 .6443 .6480 .6517
0 z 0.4 .6554 .6591 .6628 .6664 .6700 .6736 .6772 .6808 .6844 .6879
0.5 .6915 .6950 .6985 .7019 .7054 .7088 .7123 .7157 .7190 .7224
Table entry for z is the area to the left 0.6 .7257 .7291 .7324 .7357 .7389 .7422 .7454 .7486 .7517 .7549
of z. 0.7 .7580 .7611 .7642 .7673 .7704 .7734 .7764 .7794 .7823 .7852
0.8 .7881 .7910 .7939 .7967 .7995 .8023 .8051 .8078 .8106 .8133
0.9 .8159 .8186 .8212 .8238 .8264 .8289 .8315 .8340 .8365 .8389
1.0 .8413 .8438 .8461 .8485 .8508 .8531 .8554 .8577 .8599 .8621
1.1 .8643 .8665 .8686 .8708 .8729 .8749 .8770 .8790 .8810 .8830
1.2 .8849 .8869 .8888 .8907 .8925 .8944 .8962 .8980 .8997 .9015
1.3 .9032 .9049 .9066 .9082 .9099 .9115 .9131 .9147 .9162 .9177
1.4 .9192 .9207 .9222 .9236 .9251 .9265 .9279 .9292 .9306 .9319
1.5 .9332 .9345 .9357 .9370 .9382 .9394 .9406 .9418 .9429 .9441
1.6 .9452 .9463 .9474 .9484 .9495 .9505 .9515 .9525 .9535 .9545
1.7 .9554 .9564 .9573 .9582 .9591 .9599 .9608 .9616 .9625 .9633
1.8 .9641 .9649 .9656 .9664 .9671 .9678 .9686 .9693 .9699 .9706
1.9 .9713 .9719 .9726 .9732 .9738 .9744 .9750 .9756 .9761 .9767
2.0 .9772 .9778 .9783 .9788 .9793 .9798 .9803 .9808 .9812 .9817
2.1 .9821 .9826 .9830 .9834 .9838 .9842 .9846 .9850 .9854 .9857
2.2 .9861 .9864 .9868 .9871 .9875 .9878 .9881 .9884 .9887 .9890
2.3 .9893 .9896 .9898 .9901 .9904 .9906 .9909 .9911 .9913 .9916
2.4 .9918 .9920 .9922 .9925 .9927 .9929 .9931 .9932 .9934 .9936
2.5 .9938 .9940 .9941 .9943 .9945 .9946 .9948 .9949 .9951 .9952
2.6 .9953 .9955 .9956 .9957 .9959 .9960 .9961 .9962 .9963 .9964
2.7 .9965 .9966 .9967 .9968 .9969 .9970 .9971 .9972 .9973 .9974
2.8 .9974 .9975 .9976 .9977 .9977 .9978 .9979 .9979 .9980 .9981
2.9 .9981 .9982 .9982 .9983 .9984 .9984 .9985 .9985 .9986 .9986
3.0 .9987 .9987 .9987 .9988 .9988 .9989 .9989 .9989 .9990 .9990
3.1 .9990 .9991 .9991 .9991 .9992 .9992 .9992 .9992 .9993 .9993
3.2 .9993 .9993 .9994 .9994 .9994 .9994 .9994 .9995 .9995 .9995
3.3 .9995 .9995 .9995 .9996 .9996 .9996 .9996 .9996 .9996 .9997
Areas of a Standard
Normal Distribution continued 3.4 .9997 .9997 .9997 .9997 .9997 .9997 .9997 .9997 .9997 .9998
For z values greater than 3.49, use 1.000 to approximate the area.
(b) Confidence Interval
Critical Values zc
Level of Critical
Confidence c Value zc
0.70, or 70% 1.04
0.75, or 75% 1.15 Areas of a Standard Normal Distribution continued
0.80, or 80% 1.28 (c) Hypothesis Testing, Critical Values z0
0.85, or 85% 1.44
Level of Significance a 5 0.05 a 5 0.01
0.90, or 90% 1.645
0.95, or 95% 1.96 Critical value z 0 for a left-tailed test 21.645 22.33
0.98, or 98% 2.33 Critical value z 0 for a right-tailed test 1.645 2.33
0.99, or 99% 2.58 Critical values 6 z 0 for a two-tailed test 61.96 62.58
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