POSITIVE z Scores | Standard Normal (z) Distribution: Cumulative Area from the LEFT .00 .01 .02 .03 .04 05 .06 07 .08 .09 0.0 .5000 5040 .5080 .5120 5160 5199 5239 5270 5319 .5359 0.1 .5398 5438 .5478 .5517 .5557 5596 5636 .5675 5714 .5753 0.2 .5793 5832 .5871 .5910 5048 5987 .6026 .8084 6103 .8141 0.3 .8179 .6217 .8255 .8293 .6331 .6368 .6406 .8443 .6480 .8517 0.4 .8554 .6591 .8828 .6664 .6700 .6736 .6772 .6808 6844 .8879 0.5 .6915 .6950 .8985 .7019 .7054 7088 .7123 .7157 .7190 .7224 0.6 .7257 .7291 .7324 .7357 .7389 .7422 .7454 .7486 .7517 .7549 0.7 .7580 .7811 .7642 .7873 .7704 7734 .7764 .7794 .7823 .7852 0.8 .7881 .7910 .7939 .7967 7905 8023 8051 .8078 8106 .8133 0.9 8150 .8188 .8212 .8238 8264 8289 .8315 .8340 .8365 .8389 1.0 .8413 8438 .8481 .8485 8508 8531 8554 .8577 8599 .8821 1.1 .8843 .8665 .8886 .8708 8729 8749 8770 .8790 .8810 .8830 1.2 .8849 .8889 .8888 .8907 8925 8944 8962 .8980 8997 .9015 1.3 .9032 9049 .9068 .9082 9099 9115 .9131 .9147 .9182 .9177 1.4 .9192 .9207 .9222 .9236 9251 9265 9279 .9292 .9306 .9319 1.5 .9332 9345 .9357 .9370 .9382 .9394 9400 .9418 9429 .9441 1.6 .9452 .9483 .9474 .9484 9495 .9505 .9515 .9525 9535 .9545 1.7 .9554 .9564 9573 .9582 .9501 9599 9608 .9616 .9625 9833 1.8 .9841 .9849 .9656 .9664 .9671 .9678 9686 .9603 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 9001 9904 9906 9909 .9011 .9913 .9016 2.4 .9918 .9920 .9922 .9925 9927 9929 9931 .9032 9934 .9936 2.5 .9938 9940 .9941 .9943 9045 9948 .9948 .9049 .9951 .9952 2.6 .9953 .9955 .9956 .9957 .9959 .9960 9961 .9062 9963 .9964 2.7 .9965 .9908 .9967 .9968 .9969 9970 .9971 .9072 .9973 .9974 2.8 .9974 .9975 .9976 .9977 9977 .9978 .9979 .9079 9980 .9981 2.9 .9981 .9982 .9982 .9983 9984 .9984 9985 .9085 .9988 .9986 3.0 .9987 .9987 .9987 .9988 9988 .9989 9989 .9089 9090 .9990 3.1 9090 .9991 .9991 9901 .9092 .9092 .9992 .9002 .90026 .9003 3.2 .9993 .9993 .9994 .9994 9994 .9094 .9994 .9005 9095 .9995 3.3 .9995 9995 .9995 .9996 .9998 .9098 9996 .9096 .9096 .9997 3.4 .9997 .9997 .9997 .9997 9007 .9097 9007 .9007 9997 9008 3.5 use .9009 for areas above 3.49 and higher NEGATIVE z Scores Standard Normal (z) Distribution: Cumulative Area from the LEFT .00 .01 .02 .03 .04 .05 .06 .07 .08 (0' -3.5 use 0.0001 for areas below -3.48 and lower -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 .0011 .0011 .0011 .0010 .0010 -2.9 .0019 .0018 .0018 .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 .0030 .0038 .0037 .0036 -2.5 .0062 .0080 .0050 .0057 .0055 .0054 .0052 .0051 .0049 .0048 -2.4 .0082 .0080 .0078 .0075 .0073 .0071 .0069 .0068 .0088 .0084 -2.3 .0107 .0104 .0102 .0009 .0096 .0004 .0001 .0089 .0087 .0084 -2.2 .0139 .0136 .0132 .0129 .0125 .0122 .0119 .0116 .0113 .0110 -2.1 .0179 .0174 .0170 .0166 .0182 .0158 .0154 .0150 .0146 .0143 -2.0 .0228 .0222 .0217 .0212 .0207 .0202 .0197 .0102 .0188 .0183 -1.9 .0287 0281 .0274 0268 .0262 .0256 .0250 .0244 .0239 .0233 -1.8 .0350 .0351 .0344 .0336 .0329 .0322 .0314 .0307 .0301 .0204 -1.7 .0446 .0436 .0427 .0418 .0409 .0401 0302 .0384 .0375 .0367 -1.6 .0548 .0537 .0526 .0516 .0505 .0495 .0485 .0475 .0465 .0455 -1.5 .0868 0655 .0843 .0830 .0818 .0808 .0504 .0582 .0571 .0550 -1.4 .0808 .0793 .0778 .0764 .0749 .0735 .0721 .0708 .0804 .0881 -1.3 .0968 .0951 .0934 .0918 .0901 .0885 .0800 .0853 .0838 .0823 -1.2 .1151 .1131 .1112 .1003 .1075 .1056 .1038 .1020 .1003 .0985 -1.1 .1357 .1335 .1314 .1292 .1271 .1251 .1230 .1210 .1190 .1170 -1.0 .1587 .1562 .1539 .1515 .1482 .1489 .1446 .1423 .1401 .1379 -0.9 .1841 -1814 .1788 .1762 .1736 .1711 .1885 .1860 .1835 .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 3400 .3372 .3336 .3300 .3264 .3228 .3192 .3156 .3121 -0.3 .3821 .3783 .3745 .3707 .3660 .3632 .3504 .3557 .3520 .3483 -0.2 4207 .4168 .4129 4090 .4052 .4013 .3974 .3936 .3897 .3850 -0.1 .4802 4562 .4522 4483 .4443 4404 .4364 4325 4286 4247 -0.0 .5000 4980 4020 4880 4840 4801 4761 4721 4681 4641
POSITIVE z Scores | Standard Normal (z) Distribution: Cumulative Area from the LEFT .00 .01 .02 .03 .04 05 .06 07 .08 .09 0.0 .5000 5040 .5080 .5120 5160 5199 5239 5270 5319 .5359 0.1 .5398 5438 .5478 .5517 .5557 5596 5636 .5675 5714 .5753 0.2 .5793 5832 .5871 .5910 5048 5987 .6026 .8084 6103 .8141 0.3 .8179 .6217 .8255 .8293 .6331 .6368 .6406 .8443 .6480 .8517 0.4 .8554 .6591 .8828 .6664 .6700 .6736 .6772 .6808 6844 .8879 0.5 .6915 .6950 .8985 .7019 .7054 7088 .7123 .7157 .7190 .7224 0.6 .7257 .7291 .7324 .7357 .7389 .7422 .7454 .7486 .7517 .7549 0.7 .7580 .7811 .7642 .7873 .7704 7734 .7764 .7794 .7823 .7852 0.8 .7881 .7910 .7939 .7967 7905 8023 8051 .8078 8106 .8133 0.9 8150 .8188 .8212 .8238 8264 8289 .8315 .8340 .8365 .8389 1.0 .8413 8438 .8481 .8485 8508 8531 8554 .8577 8599 .8821 1.1 .8843 .8665 .8886 .8708 8729 8749 8770 .8790 .8810 .8830 1.2 .8849 .8889 .8888 .8907 8925 8944 8962 .8980 8997 .9015 1.3 .9032 9049 .9068 .9082 9099 9115 .9131 .9147 .9182 .9177 1.4 .9192 .9207 .9222 .9236 9251 9265 9279 .9292 .9306 .9319 1.5 .9332 9345 .9357 .9370 .9382 .9394 9400 .9418 9429 .9441 1.6 .9452 .9483 .9474 .9484 9495 .9505 .9515 .9525 9535 .9545 1.7 .9554 .9564 9573 .9582 .9501 9599 9608 .9616 .9625 9833 1.8 .9841 .9849 .9656 .9664 .9671 .9678 9686 .9603 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 9001 9904 9906 9909 .9011 .9913 .9016 2.4 .9918 .9920 .9922 .9925 9927 9929 9931 .9032 9934 .9936 2.5 .9938 9940 .9941 .9943 9045 9948 .9948 .9049 .9951 .9952 2.6 .9953 .9955 .9956 .9957 .9959 .9960 9961 .9062 9963 .9964 2.7 .9965 .9908 .9967 .9968 .9969 9970 .9971 .9072 .9973 .9974 2.8 .9974 .9975 .9976 .9977 9977 .9978 .9979 .9079 9980 .9981 2.9 .9981 .9982 .9982 .9983 9984 .9984 9985 .9085 .9988 .9986 3.0 .9987 .9987 .9987 .9988 9988 .9989 9989 .9089 9090 .9990 3.1 9090 .9991 .9991 9901 .9092 .9092 .9992 .9002 .90026 .9003 3.2 .9993 .9993 .9994 .9994 9994 .9094 .9994 .9005 9095 .9995 3.3 .9995 9995 .9995 .9996 .9998 .9098 9996 .9096 .9096 .9997 3.4 .9997 .9997 .9997 .9997 9007 .9097 9007 .9007 9997 9008 3.5 use .9009 for areas above 3.49 and higher NEGATIVE z Scores Standard Normal (z) Distribution: Cumulative Area from the LEFT .00 .01 .02 .03 .04 .05 .06 .07 .08 (0' -3.5 use 0.0001 for areas below -3.48 and lower -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 .0011 .0011 .0011 .0010 .0010 -2.9 .0019 .0018 .0018 .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 .0030 .0038 .0037 .0036 -2.5 .0062 .0080 .0050 .0057 .0055 .0054 .0052 .0051 .0049 .0048 -2.4 .0082 .0080 .0078 .0075 .0073 .0071 .0069 .0068 .0088 .0084 -2.3 .0107 .0104 .0102 .0009 .0096 .0004 .0001 .0089 .0087 .0084 -2.2 .0139 .0136 .0132 .0129 .0125 .0122 .0119 .0116 .0113 .0110 -2.1 .0179 .0174 .0170 .0166 .0182 .0158 .0154 .0150 .0146 .0143 -2.0 .0228 .0222 .0217 .0212 .0207 .0202 .0197 .0102 .0188 .0183 -1.9 .0287 0281 .0274 0268 .0262 .0256 .0250 .0244 .0239 .0233 -1.8 .0350 .0351 .0344 .0336 .0329 .0322 .0314 .0307 .0301 .0204 -1.7 .0446 .0436 .0427 .0418 .0409 .0401 0302 .0384 .0375 .0367 -1.6 .0548 .0537 .0526 .0516 .0505 .0495 .0485 .0475 .0465 .0455 -1.5 .0868 0655 .0843 .0830 .0818 .0808 .0504 .0582 .0571 .0550 -1.4 .0808 .0793 .0778 .0764 .0749 .0735 .0721 .0708 .0804 .0881 -1.3 .0968 .0951 .0934 .0918 .0901 .0885 .0800 .0853 .0838 .0823 -1.2 .1151 .1131 .1112 .1003 .1075 .1056 .1038 .1020 .1003 .0985 -1.1 .1357 .1335 .1314 .1292 .1271 .1251 .1230 .1210 .1190 .1170 -1.0 .1587 .1562 .1539 .1515 .1482 .1489 .1446 .1423 .1401 .1379 -0.9 .1841 -1814 .1788 .1762 .1736 .1711 .1885 .1860 .1835 .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 3400 .3372 .3336 .3300 .3264 .3228 .3192 .3156 .3121 -0.3 .3821 .3783 .3745 .3707 .3660 .3632 .3504 .3557 .3520 .3483 -0.2 4207 .4168 .4129 4090 .4052 .4013 .3974 .3936 .3897 .3850 -0.1 .4802 4562 .4522 4483 .4443 4404 .4364 4325 4286 4247 -0.0 .5000 4980 4020 4880 4840 4801 4761 4721 4681 4641
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
Related questions
Concept explainers
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
Topic Video
Question
100%
A teacher says that the top 14% of the class received an A on the last test. The scores were normally distributed with mean 67 and standard deviation
18.
Find the minimum score required to get an A.
Round to the whole number.
Transcribed Image Text:POSITIVE z Scores
| Standard Normal (z) Distribution: Cumulative Area from the LEFT
.00
.01
.02
.03
.04
05
.06
07
.08
.09
0.0
.5000
5040
.5080
.5120
5160
5199
5239
5270
5319
.5359
0.1
.5398
5438
.5478
.5517
.5557
5596
5636
.5675
5714
.5753
0.2
.5793
5832
.5871
.5910
5048
5987
.6026
.8084
6103
.8141
0.3
.8179
.6217
.8255
.8293
.6331
.6368
.6406
.8443
.6480
.8517
0.4
.8554
.6591
.8828
.6664
.6700
.6736
.6772
.6808
6844
.8879
0.5
.6915
.6950
.8985
.7019
.7054
7088
.7123
.7157
.7190
.7224
0.6
.7257
.7291
.7324
.7357
.7389
.7422
.7454
.7486
.7517
.7549
0.7
.7580
.7811
.7642
.7873
.7704
7734
.7764
.7794
.7823
.7852
0.8
.7881
.7910
.7939
.7967
7905
8023
8051
.8078
8106
.8133
0.9
8150
.8188
.8212
.8238
8264
8289
.8315
.8340
.8365
.8389
1.0
.8413
8438
.8481
.8485
8508
8531
8554
.8577
8599
.8821
1.1
.8843
.8665
.8886
.8708
8729
8749
8770
.8790
.8810
.8830
1.2
.8849
.8889
.8888
.8907
8925
8944
8962
.8980
8997
.9015
1.3
.9032
9049
.9068
.9082
9099
9115
.9131
.9147
.9182
.9177
1.4
.9192
.9207
.9222
.9236
9251
9265
9279
.9292
.9306
.9319
1.5
.9332
9345
.9357
.9370
.9382
.9394
9400
.9418
9429
.9441
1.6
.9452
.9483
.9474
.9484
9495
.9505
.9515
.9525
9535
.9545
1.7
.9554
.9564
9573
.9582
.9501
9599
9608
.9616
.9625
9833
1.8
.9841
.9849
.9656
.9664
.9671
.9678
9686
.9603
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
9001
9904
9906
9909
.9011
.9913
.9016
2.4
.9918
.9920
.9922
.9925
9927
9929
9931
.9032
9934
.9936
2.5
.9938
9940
.9941
.9943
9045
9948
.9948
.9049
.9951
.9952
2.6
.9953
.9955
.9956
.9957
.9959
.9960
9961
.9062
9963
.9964
2.7
.9965
.9908
.9967
.9968
.9969
9970
.9971
.9072
.9973
.9974
2.8
.9974
.9975
.9976
.9977
9977
.9978
.9979
.9079
9980
.9981
2.9
.9981
.9982
.9982
.9983
9984
.9984
9985
.9085
.9988
.9986
3.0
.9987
.9987
.9987
.9988
9988
.9989
9989
.9089
9090
.9990
3.1
9090
.9991
.9991
9901
.9092
.9092
.9992
.9002
.90026
.9003
3.2
.9993
.9993
.9994
.9994
9994
.9094
.9994
.9005
9095
.9995
3.3
.9995
9995
.9995
.9996
.9998
.9098
9996
.9096
.9096
.9997
3.4
.9997
.9997
.9997
.9997
9007
.9097
9007
.9007
9997
9008
3.5
use .9009 for areas above 3.49
and higher
Transcribed Image Text:NEGATIVE z Scores
Standard Normal (z) Distribution: Cumulative Area from the LEFT
.00
.01
.02
.03
.04
.05
.06
.07
.08
(0'
-3.5
use 0.0001 for areas below -3.48
and lower
-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
.0011
.0011
.0011
.0010
.0010
-2.9
.0019
.0018
.0018
.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
.0030
.0038
.0037
.0036
-2.5
.0062
.0080
.0050
.0057
.0055
.0054
.0052
.0051
.0049
.0048
-2.4
.0082
.0080
.0078
.0075
.0073
.0071
.0069
.0068
.0088
.0084
-2.3
.0107
.0104
.0102
.0009
.0096
.0004
.0001
.0089
.0087
.0084
-2.2
.0139
.0136
.0132
.0129
.0125
.0122
.0119
.0116
.0113
.0110
-2.1
.0179
.0174
.0170
.0166
.0182
.0158
.0154
.0150
.0146
.0143
-2.0
.0228
.0222
.0217
.0212
.0207
.0202
.0197
.0102
.0188
.0183
-1.9
.0287
0281
.0274
0268
.0262
.0256
.0250
.0244
.0239
.0233
-1.8
.0350
.0351
.0344
.0336
.0329
.0322
.0314
.0307
.0301
.0204
-1.7
.0446
.0436
.0427
.0418
.0409
.0401
0302
.0384
.0375
.0367
-1.6
.0548
.0537
.0526
.0516
.0505
.0495
.0485
.0475
.0465
.0455
-1.5
.0868
0655
.0843
.0830
.0818
.0808
.0504
.0582
.0571
.0550
-1.4
.0808
.0793
.0778
.0764
.0749
.0735
.0721
.0708
.0804
.0881
-1.3
.0968
.0951
.0934
.0918
.0901
.0885
.0800
.0853
.0838
.0823
-1.2
.1151
.1131
.1112
.1003
.1075
.1056
.1038
.1020
.1003
.0985
-1.1
.1357
.1335
.1314
.1292
.1271
.1251
.1230
.1210
.1190
.1170
-1.0
.1587
.1562
.1539
.1515
.1482
.1489
.1446
.1423
.1401
.1379
-0.9
.1841
-1814
.1788
.1762
.1736
.1711
.1885
.1860
.1835
.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
3400
.3372
.3336
.3300
.3264
.3228
.3192
.3156
.3121
-0.3
.3821
.3783
.3745
.3707
.3660
.3632
.3504
.3557
.3520
.3483
-0.2
4207
.4168
.4129
4090
.4052
.4013
.3974
.3936
.3897
.3850
-0.1
.4802
4562
.4522
4483
.4443
4404
.4364
4325
4286
4247
-0.0
.5000
4980
4020
4880
4840
4801
4761
4721
4681
4641
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