The scores on a finite mathematics test were normally distributed with a mean of 77 and a standard deviation of 8. [a] The minimum score a student could obtain in order to receive an A is 90. What is the probability a randomly selected student receives an A? [b] The minimum score a student could obtain in order to pass the test is 60. What is the probability a randomly selected student failed the test? NEGATIVE z Scores POSITIVE z Scores Standard Normal (z) Distribution: Cumulative Area from the LEFT Standard Normal (z) Distribution: Cumulative Area from the LEFT .00 .01 .02 .03 .04 .05 .06 .07 .08 .09 .00 .01 .02 .03 .04 .05 .06 07 08 .00 -3.5 use 0.0001 for areas below -3.49 0.0 .5000 5040 .5080 .5120 5160 5199 5239 .5270 5319 .5359 and lower -3.4 0003 .0003 .0003 .0003 .0003 .0003 .0003 .0003 .0003 .0002 0.1 .5398 5438 5478 .5517 5557 5596 5636 5675 .5714 .5753 0.2 .5793 5832 .5871 .5010 5948 5987 6026 .6084 6103 .8141 -3.3 .0005 .0005 .0005 .0004 .0004 .0004 .0004 .0004 .0004 .0003 0.3 8179 6217 .8255 .8293 6331 6368 6406 .8443 .8480 R490 .8517 -3.2 .0007 .0007 .0008 .0006 .0008 .0006 .0008 .0005 .0005 .0005 0.4 .6554 .6591 .8828 .8884 6700 6738 .6772 .6808 .6844 .8879 -3.1 .0010 .0009 .0009 .0009 .0008 .0008 .0008 .0008 .0007 .0007 0.5 .8915 .6950 .8985 .7019 7054 7088 .7123 .7157 .7190 .7224 -3.0 .0013 .0013 .0013 .0012 .0012 .0011 .0011 .0011 .0010 .0010 0.6 .7257 .7291 .7324 .7357 .7389 .7422 .7454 .7486 .7517 .7549 -2.9 .0019 .0018 .0018 .0017 .0016 .0016 .0015 .0015 .0014 .0014 0.7 .7580 7811 .7842 .7673 .7704 7734 .7764 .7794 .7823 .7852 -2.8 .0026 .0025 .0024 .0023 .0023 .0022 .0021 .0021 .0020 .0019 0.8 .7881 .7910 .7939 .7967 .7995 8023 8051 .8078 8106 .8133 -2.7 .0035 .0034 .0033 .0032 .0031 .0030 .0020 .0028 .0027 .0026 0.9 .8159 8188 .8212 .8238 8264 8289 8315 .8340 .8365 .8389 -2.6 .0047 .0045 .0044 .0043 .0041 .0040 .0030 .0038 .0037 .0036 1.0 .8413 8438 .8461 .8485 8508 .8531 8554 .8577 8599 .8821 -2.5 .0062 .0060 .0050 .0057 .0055 .0054 .0052 .0051 .0049 .0048 1.1 .8843 8885 .8886 8708 8729 8749 8770 .8790 8810 8830 -2.4 .0082 .0080 .0078 .0075 .0073 .0071 .0060 .0068 .0068 .0064 1.2 .8849 8809 .8888 .8907 8925 .8944 8962 .8980 .8997 9015 czeo 9009 ZO8O- -2.3 .0107 .0104 .0102 .0000 .0096 .0004 .0001 .0089 .0087 .0084 1.3 .9032 9049 .9006 .9082 9115 9131 .9147 9182 9177 -2.2 .0139 .0136 .0132 .0129 .0125 .0122 .0119 .0116 .0113 .0110 1.4 .9192 9207 9222 9251 9265 9279 .9292 9306 .9319 9230 -2.1 .0179 .0174 .0170 .0166 .0162 .0158 .0154 .0150 .0146 .0143 1.5 .9332 9345 .9357 .9370 9382 9394 9406 .9429 .9441 9418 -2.0 .0228 .0222 .0217 .0212 .0207 .0202 .0197 .0192 .0188 .0183 1.6 9452 9483 9474 9484 9495 9505 9515 .9525 9535 .9545 -1.9 .0287 .0281 .0274 .0268 .0262 .0256 .0250 .0244 .0230 .0233 17 9554 .9584 .9573 .9582 9501 9509 9608 .9616 O818 .9625 .9833 -1.8 .0350 .0351 .0344 .0336 .0329 .0322 .0314 .0307 .0301 .0204 1.8 9641 9840 .9856 .9664 9671 .9678 9688 .9003 9699 .9706 -1.7 .0446 .0436 .0427 .0418 .0400 .0401 .0392 .0384 .0375 .0367 1.9 .9713 9719 .9726 .9732 9738 .9744 9750 .9756 9761 9767 -1.6 .0548 .0537 .0526 .0516 .0505 .0495 .0485 .0475 .0465 .0455 2.0 .9772 9778 .9783 .9788 9793 9798 9803 .9808 9812 9817 -1.5 .0868 .0855 .0643 .0830 .0618 .0806 .0504 .0582 .0571 .0550 2.1 .9821 9826 .9830 .9834 9838 .9842 9848 .9850 9854 9857 -1.4 .0808 .0793 .0778 .0764 .0749 .0735 .0721 .0708 .0604 .0881 22 .9861 .9884 .9888 .9871 9875 .9878 9881 .9884 .9887 .9890 -1.3 .0968 .0951 .0934 .0918 .0901 .0885 .0880 .0853 .0838 .0823 2.3 .9893 .9896 .9898 .9901 9904 9906 9909 2011 .9913 .9916 -1.2 .1151 .1131 .1112 .1003 .1075 1056 .1038 .1020 .1003 .0985 2.4 .9918 9920 .9922 .9925 9927 9929 9931 .9932 .9934 .9936 2.5 9938 .9940 .9941 .9943 0043 9945 9946 .9948 .9049 9951 .9952 -1.1 .1357 .1335 .1314 .1292 .1271 .1251 .1230 .1210 .1190 .1170 2.6 .9953 .9955 .9956 .9957 9959 9960 9961 .9062 .9963 .9964 -1.0 .1587 .1562 .1530 .1515 .1492 .1489 .1446 .1423 .1401 .1379 2.7 .9965 .9988 .9967 9969 0087 .9908 9970 9971 .9072 .9973 .9974 -0.9 .1841 .1814 .1788 .1762 .1736 1711 .1685 .1660 .1835 .1811 2.8 .9974 .9975 .9976 .9977 9977 9978 9979 .9079 .9980 .9981 -0.8 2119 .2090 2061 2033 .2005 .1977 .1949 .1922 .1894 .1867 2.9 .9981 .9982 .9982 .9983 9984 9084 9985 .9085 9986 .9986 -0.7 2420 2389 2358 2327 2206 2266 2236 2206 .2177 2148 3.0 .9987 .9987 .9987 .9988 9988 .9989 9989 .9089 .9990 .9990 -0.6 2743 2709 .2676 2643 .2611 .2578 2546 2514 2483 2451 3.1 .9990 .9991 9001 .9991 9992 .9992 9992 .9092 .90026 .9003 -0.5 3085 .3050 .3015 2981 2946 2912 2877 2843 2810 2776 3.2 .9993 .9993 .9094 .9994 9994 9904 9994 .9005 .9005 .9995 -0.4 3446 3400 .3372 3336 .3300 .3264 .3228 3192 .3156 .3121 3.3 .9995 .9995 .9005 .9996 9998 9090 9990 .9096 .9096 .9997 -0.3 .3821 3783 .3745 3707 .3660 3832 .3504 3557 3520 3483 3.4 .9997 9997 .9997 .9997 9997 .9097 9997 .9097 .9097 .9908 -0.2 4207 4168 4129 4090 .4052 4013 .3974 .3936 .3897 3850 3.5 use .9009 for areas above 3.49 -0.1 .4602 4562 .4522 4483 4443 4404 4364 4325 4286 4247 and higher -0.0 5000 4960 4920 4880 4840 4801 4761 4721 4681 4641
The scores on a finite mathematics test were normally distributed with a mean of 77 and a standard deviation of 8. [a] The minimum score a student could obtain in order to receive an A is 90. What is the probability a randomly selected student receives an A? [b] The minimum score a student could obtain in order to pass the test is 60. What is the probability a randomly selected student failed the test? NEGATIVE z Scores POSITIVE z Scores Standard Normal (z) Distribution: Cumulative Area from the LEFT Standard Normal (z) Distribution: Cumulative Area from the LEFT .00 .01 .02 .03 .04 .05 .06 .07 .08 .09 .00 .01 .02 .03 .04 .05 .06 07 08 .00 -3.5 use 0.0001 for areas below -3.49 0.0 .5000 5040 .5080 .5120 5160 5199 5239 .5270 5319 .5359 and lower -3.4 0003 .0003 .0003 .0003 .0003 .0003 .0003 .0003 .0003 .0002 0.1 .5398 5438 5478 .5517 5557 5596 5636 5675 .5714 .5753 0.2 .5793 5832 .5871 .5010 5948 5987 6026 .6084 6103 .8141 -3.3 .0005 .0005 .0005 .0004 .0004 .0004 .0004 .0004 .0004 .0003 0.3 8179 6217 .8255 .8293 6331 6368 6406 .8443 .8480 R490 .8517 -3.2 .0007 .0007 .0008 .0006 .0008 .0006 .0008 .0005 .0005 .0005 0.4 .6554 .6591 .8828 .8884 6700 6738 .6772 .6808 .6844 .8879 -3.1 .0010 .0009 .0009 .0009 .0008 .0008 .0008 .0008 .0007 .0007 0.5 .8915 .6950 .8985 .7019 7054 7088 .7123 .7157 .7190 .7224 -3.0 .0013 .0013 .0013 .0012 .0012 .0011 .0011 .0011 .0010 .0010 0.6 .7257 .7291 .7324 .7357 .7389 .7422 .7454 .7486 .7517 .7549 -2.9 .0019 .0018 .0018 .0017 .0016 .0016 .0015 .0015 .0014 .0014 0.7 .7580 7811 .7842 .7673 .7704 7734 .7764 .7794 .7823 .7852 -2.8 .0026 .0025 .0024 .0023 .0023 .0022 .0021 .0021 .0020 .0019 0.8 .7881 .7910 .7939 .7967 .7995 8023 8051 .8078 8106 .8133 -2.7 .0035 .0034 .0033 .0032 .0031 .0030 .0020 .0028 .0027 .0026 0.9 .8159 8188 .8212 .8238 8264 8289 8315 .8340 .8365 .8389 -2.6 .0047 .0045 .0044 .0043 .0041 .0040 .0030 .0038 .0037 .0036 1.0 .8413 8438 .8461 .8485 8508 .8531 8554 .8577 8599 .8821 -2.5 .0062 .0060 .0050 .0057 .0055 .0054 .0052 .0051 .0049 .0048 1.1 .8843 8885 .8886 8708 8729 8749 8770 .8790 8810 8830 -2.4 .0082 .0080 .0078 .0075 .0073 .0071 .0060 .0068 .0068 .0064 1.2 .8849 8809 .8888 .8907 8925 .8944 8962 .8980 .8997 9015 czeo 9009 ZO8O- -2.3 .0107 .0104 .0102 .0000 .0096 .0004 .0001 .0089 .0087 .0084 1.3 .9032 9049 .9006 .9082 9115 9131 .9147 9182 9177 -2.2 .0139 .0136 .0132 .0129 .0125 .0122 .0119 .0116 .0113 .0110 1.4 .9192 9207 9222 9251 9265 9279 .9292 9306 .9319 9230 -2.1 .0179 .0174 .0170 .0166 .0162 .0158 .0154 .0150 .0146 .0143 1.5 .9332 9345 .9357 .9370 9382 9394 9406 .9429 .9441 9418 -2.0 .0228 .0222 .0217 .0212 .0207 .0202 .0197 .0192 .0188 .0183 1.6 9452 9483 9474 9484 9495 9505 9515 .9525 9535 .9545 -1.9 .0287 .0281 .0274 .0268 .0262 .0256 .0250 .0244 .0230 .0233 17 9554 .9584 .9573 .9582 9501 9509 9608 .9616 O818 .9625 .9833 -1.8 .0350 .0351 .0344 .0336 .0329 .0322 .0314 .0307 .0301 .0204 1.8 9641 9840 .9856 .9664 9671 .9678 9688 .9003 9699 .9706 -1.7 .0446 .0436 .0427 .0418 .0400 .0401 .0392 .0384 .0375 .0367 1.9 .9713 9719 .9726 .9732 9738 .9744 9750 .9756 9761 9767 -1.6 .0548 .0537 .0526 .0516 .0505 .0495 .0485 .0475 .0465 .0455 2.0 .9772 9778 .9783 .9788 9793 9798 9803 .9808 9812 9817 -1.5 .0868 .0855 .0643 .0830 .0618 .0806 .0504 .0582 .0571 .0550 2.1 .9821 9826 .9830 .9834 9838 .9842 9848 .9850 9854 9857 -1.4 .0808 .0793 .0778 .0764 .0749 .0735 .0721 .0708 .0604 .0881 22 .9861 .9884 .9888 .9871 9875 .9878 9881 .9884 .9887 .9890 -1.3 .0968 .0951 .0934 .0918 .0901 .0885 .0880 .0853 .0838 .0823 2.3 .9893 .9896 .9898 .9901 9904 9906 9909 2011 .9913 .9916 -1.2 .1151 .1131 .1112 .1003 .1075 1056 .1038 .1020 .1003 .0985 2.4 .9918 9920 .9922 .9925 9927 9929 9931 .9932 .9934 .9936 2.5 9938 .9940 .9941 .9943 0043 9945 9946 .9948 .9049 9951 .9952 -1.1 .1357 .1335 .1314 .1292 .1271 .1251 .1230 .1210 .1190 .1170 2.6 .9953 .9955 .9956 .9957 9959 9960 9961 .9062 .9963 .9964 -1.0 .1587 .1562 .1530 .1515 .1492 .1489 .1446 .1423 .1401 .1379 2.7 .9965 .9988 .9967 9969 0087 .9908 9970 9971 .9072 .9973 .9974 -0.9 .1841 .1814 .1788 .1762 .1736 1711 .1685 .1660 .1835 .1811 2.8 .9974 .9975 .9976 .9977 9977 9978 9979 .9079 .9980 .9981 -0.8 2119 .2090 2061 2033 .2005 .1977 .1949 .1922 .1894 .1867 2.9 .9981 .9982 .9982 .9983 9984 9084 9985 .9085 9986 .9986 -0.7 2420 2389 2358 2327 2206 2266 2236 2206 .2177 2148 3.0 .9987 .9987 .9987 .9988 9988 .9989 9989 .9089 .9990 .9990 -0.6 2743 2709 .2676 2643 .2611 .2578 2546 2514 2483 2451 3.1 .9990 .9991 9001 .9991 9992 .9992 9992 .9092 .90026 .9003 -0.5 3085 .3050 .3015 2981 2946 2912 2877 2843 2810 2776 3.2 .9993 .9993 .9094 .9994 9994 9904 9994 .9005 .9005 .9995 -0.4 3446 3400 .3372 3336 .3300 .3264 .3228 3192 .3156 .3121 3.3 .9995 .9995 .9005 .9996 9998 9090 9990 .9096 .9096 .9997 -0.3 .3821 3783 .3745 3707 .3660 3832 .3504 3557 3520 3483 3.4 .9997 9997 .9997 .9997 9997 .9097 9997 .9097 .9097 .9908 -0.2 4207 4168 4129 4090 .4052 4013 .3974 .3936 .3897 3850 3.5 use .9009 for areas above 3.49 -0.1 .4602 4562 .4522 4483 4443 4404 4364 4325 4286 4247 and higher -0.0 5000 4960 4920 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...
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Concept explainers
Addition Rule of Probability
It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.
Expected Value
When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).
Probability Distributions
Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.
Basic Probability
The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.
Topic Video
Question
100%
What formula do I use?
![The scores on a finite mathematics test were normally distributed with a mean of 77 and
a standard deviation of 8.
[a] The minimum score a student could obtain in order to receive an A is 90. What is
the probability a randomly selected student receives an A?
[b] The minimum score a student could obtain in order to pass the test is 60. What is
the probability a randomly selected student failed the test?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb5e70e13-ab42-427e-a89a-b94f00f72dd9%2Fd773b1b9-dff1-4f1c-8a58-0a19d673aab7%2F4tux0h.png&w=3840&q=75)
Transcribed Image Text:The scores on a finite mathematics test were normally distributed with a mean of 77 and
a standard deviation of 8.
[a] The minimum score a student could obtain in order to receive an A is 90. What is
the probability a randomly selected student receives an A?
[b] The minimum score a student could obtain in order to pass the test is 60. What is
the probability a randomly selected student failed the test?
Transcribed Image Text:NEGATIVE z Scores
POSITIVE z Scores
Standard Normal (z) Distribution: Cumulative Area from the LEFT
Standard Normal (z) Distribution: Cumulative Area from the LEFT
.00
.01
.02
.03
.04
.05
.06
.07
.08
.09
.00
.01
.02
.03
.04
.05
.06
07
08
.00
-3.5
use 0.0001 for areas below -3.49
0.0
.5000
5040
.5080
.5120
5160
5199
5239
.5270
5319
.5359
and lower
-3.4
0003
.0003
.0003
.0003
.0003
.0003
.0003
.0003
.0003
.0002
0.1
.5398
5438
5478
.5517
5557
5596
5636
5675
.5714
.5753
0.2
.5793
5832
.5871
.5010
5948
5987
6026
.6084
6103
.8141
-3.3
.0005
.0005
.0005
.0004
.0004
.0004
.0004
.0004
.0004
.0003
0.3
8179
6217
.8255
.8293
6331
6368
6406
.8443
.8480
R490
.8517
-3.2
.0007
.0007
.0008
.0006
.0008
.0006
.0008
.0005
.0005
.0005
0.4
.6554
.6591
.8828
.8884
6700
6738
.6772
.6808
.6844
.8879
-3.1
.0010
.0009
.0009
.0009
.0008
.0008
.0008
.0008
.0007
.0007
0.5
.8915
.6950
.8985
.7019
7054
7088
.7123
.7157
.7190
.7224
-3.0
.0013
.0013
.0013
.0012
.0012
.0011
.0011
.0011
.0010
.0010
0.6
.7257
.7291
.7324
.7357
.7389
.7422
.7454
.7486
.7517
.7549
-2.9
.0019
.0018
.0018
.0017
.0016
.0016
.0015
.0015
.0014
.0014
0.7
.7580
7811
.7842
.7673
.7704
7734
.7764
.7794
.7823
.7852
-2.8
.0026
.0025
.0024
.0023
.0023
.0022
.0021
.0021
.0020
.0019
0.8
.7881
.7910
.7939
.7967
.7995
8023
8051
.8078
8106
.8133
-2.7
.0035
.0034
.0033
.0032
.0031
.0030
.0020
.0028
.0027
.0026
0.9
.8159
8188
.8212
.8238
8264
8289
8315
.8340
.8365
.8389
-2.6
.0047
.0045
.0044
.0043
.0041
.0040
.0030
.0038
.0037
.0036
1.0
.8413
8438
.8461
.8485
8508
.8531
8554
.8577
8599
.8821
-2.5
.0062
.0060
.0050
.0057
.0055
.0054
.0052
.0051
.0049
.0048
1.1
.8843
8885
.8886
8708
8729
8749
8770
.8790
8810
8830
-2.4
.0082
.0080
.0078
.0075
.0073
.0071
.0060
.0068
.0068
.0064
1.2
.8849
8809
.8888
.8907
8925
.8944
8962
.8980
.8997
9015
czeo
9009
ZO8O-
-2.3
.0107
.0104
.0102
.0000
.0096
.0004
.0001
.0089
.0087
.0084
1.3
.9032
9049
.9006
.9082
9115
9131
.9147
9182
9177
-2.2
.0139
.0136
.0132
.0129
.0125
.0122
.0119
.0116
.0113
.0110
1.4
.9192
9207
9222
9251
9265
9279
.9292
9306
.9319
9230
-2.1
.0179
.0174
.0170
.0166
.0162
.0158
.0154
.0150
.0146
.0143
1.5
.9332
9345
.9357
.9370
9382
9394
9406
.9429
.9441
9418
-2.0
.0228
.0222
.0217
.0212
.0207
.0202
.0197
.0192
.0188
.0183
1.6
9452
9483
9474
9484
9495
9505
9515
.9525
9535
.9545
-1.9
.0287
.0281
.0274
.0268
.0262
.0256
.0250
.0244
.0230
.0233
17
9554
.9584
.9573
.9582
9501
9509
9608
.9616
O818
.9625
.9833
-1.8
.0350
.0351
.0344
.0336
.0329
.0322
.0314
.0307
.0301
.0204
1.8
9641
9840
.9856
.9664
9671
.9678
9688
.9003
9699
.9706
-1.7
.0446
.0436
.0427
.0418
.0400
.0401
.0392
.0384
.0375
.0367
1.9
.9713
9719
.9726
.9732
9738
.9744
9750
.9756
9761
9767
-1.6
.0548
.0537
.0526
.0516
.0505
.0495
.0485
.0475
.0465
.0455
2.0
.9772
9778
.9783
.9788
9793
9798
9803
.9808
9812
9817
-1.5
.0868
.0855
.0643
.0830
.0618
.0806
.0504
.0582
.0571
.0550
2.1
.9821
9826
.9830
.9834
9838
.9842
9848
.9850
9854
9857
-1.4
.0808
.0793
.0778
.0764
.0749
.0735
.0721
.0708
.0604
.0881
22
.9861
.9884
.9888
.9871
9875
.9878
9881
.9884
.9887
.9890
-1.3
.0968
.0951
.0934
.0918
.0901
.0885
.0880
.0853
.0838
.0823
2.3
.9893
.9896
.9898
.9901
9904
9906
9909
2011
.9913
.9916
-1.2
.1151
.1131
.1112
.1003
.1075
1056
.1038
.1020
.1003
.0985
2.4
.9918
9920
.9922
.9925
9927
9929
9931
.9932
.9934
.9936
2.5
9938
.9940
.9941
.9943
0043
9945
9946
.9948
.9049
9951
.9952
-1.1
.1357
.1335
.1314
.1292
.1271
.1251
.1230
.1210
.1190
.1170
2.6
.9953
.9955
.9956
.9957
9959
9960
9961
.9062
.9963
.9964
-1.0
.1587
.1562
.1530
.1515
.1492
.1489
.1446
.1423
.1401
.1379
2.7
.9965
.9988
.9967
9969
0087
.9908
9970
9971
.9072
.9973
.9974
-0.9
.1841
.1814
.1788
.1762
.1736
1711
.1685
.1660
.1835
.1811
2.8
.9974
.9975
.9976
.9977
9977
9978
9979
.9079
.9980
.9981
-0.8
2119
.2090
2061
2033
.2005
.1977
.1949
.1922
.1894
.1867
2.9
.9981
.9982
.9982
.9983
9984
9084
9985
.9085
9986
.9986
-0.7
2420
2389
2358
2327
2206
2266
2236
2206
.2177
2148
3.0
.9987
.9987
.9987
.9988
9988
.9989
9989
.9089
.9990
.9990
-0.6
2743
2709
.2676
2643
.2611
.2578
2546
2514
2483
2451
3.1
.9990
.9991
9001
.9991
9992
.9992
9992
.9092
.90026
.9003
-0.5
3085
.3050
.3015
2981
2946
2912
2877
2843
2810
2776
3.2
.9993
.9993
.9094
.9994
9994
9904
9994
.9005
.9005
.9995
-0.4
3446
3400
.3372
3336
.3300
.3264
.3228
3192
.3156
.3121
3.3
.9995
.9995
.9005
.9996
9998
9090
9990
.9096
.9096
.9997
-0.3
.3821
3783
.3745
3707
.3660
3832
.3504
3557
3520
3483
3.4
.9997
9997
.9997
.9997
9997
.9097
9997
.9097
.9097
.9908
-0.2
4207
4168
4129
4090
.4052
4013
.3974
.3936
.3897
3850
3.5
use .9009 for areas above 3.49
-0.1
.4602
4562
.4522
4483
4443
4404
4364
4325
4286
4247
and higher
-0.0
5000
4960
4920
4880
4840
4801
4761
4721
4681
4641
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