Find the area to the left of z = -1.5 Solution: Draw the normal curve and shade the required region 1 2 3 Find the area that z = -1.5 corresponds to an area corresponds to the z-value Examine the graph and use probability notation to form the equation . The proportion of the area to the left of z = -1.5 is

MATLAB: An Introduction with Applications
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Question
Find the area to the left of z = -1.5
Solution:
Draw the normal curve and
shade the required region
2 3
Find the area that
z = -1.5 corresponds to an area
corresponds to the z-value
Examine the graph and use
probability notation to form
the equation
. The proportion of the area to the left of z = -1.5 is
Transcribed Image Text:Find the area to the left of z = -1.5 Solution: Draw the normal curve and shade the required region 2 3 Find the area that z = -1.5 corresponds to an area corresponds to the z-value Examine the graph and use probability notation to form the equation . The proportion of the area to the left of z = -1.5 is
Table I: Table of Areas under the Normal Curve
06|
.00
.01
.02
.03
.04
.05
.07
.08
.09
0.0
.0000
.0040
.00so
.0120
.0150
.0199
.0239
.0279
.0319
.0359
0.1
.0398
.0438
.0478
.0517
.0557
.0596
.0636
.0675
.0714 .0754
0.2
.0793
.0832
.0871
.0910
.0948
.0987
1026
.1064
.1103.1141
0.3
.1179
.1217
.1253
.1293
.1331
.1368
.1406
.1443
.1480
.1517
0.4
.1554
.1591
.1628
.1664
.1700
.1736
.1772
.1808
.1844
.1879
0.5
.1915
.1950
.1985
.2019
.2054
.2088
.2123
.2157
.2190
.2224
0.6
.2258
.2291
.2324
.2357
2389
.2422
.2454
2486
.2518
.2549
0.7
2580
.2612
.2642
.2673
.2704
.2734
.2764
.2794
.2823
.2852
0.8
2881
.2910
.2939
.2967
2996
.3023
3051
.3078
.3106
.3133
0.9
3159
.3186
.3212
3288
3264
.3289
.3315
.3340
.3365
3389
1.0
3413
.3438
.3461
.3485
.3508
.3531
.3554
.3557
.3559 .3621
.3810 .3830
.3997 4015
1.1
.3642
.3665
.3686
.3708
.3729
.3749
.3770
.3790
1.2
.3849
.3869
.3888
.3907
.3925
.3944
.3962
.3980
1.3
4032
.4049
.4066
.4082
4099
.4115
4131
.4147
.4162 .4177
1.4
4192
.4207
.4222
4236
4251
.4265
4279
.4292
.4306
.4319
1.5
.4332
.4345
.4357
.4370
4382
.4394
.4406
.4418
.4429 .4441
1.6
.4452
.4463
.4474
.4484
4495
.4505
4515
4525
.4535 .4545
1.7
4554
.4564
.4573
.4582
4591
.4599
.4608
.4616
.4625 .4633
1.8
4641
.4649
.4656
4664
4671
.4678
4686
.4693
.4699
4706
1.9
4713
.4719
.4726
.4732
4738
.4744
.4750
.4756
.4761
.4767
2.0
4772
.4778
.4783
.4788
.4793
.4798
4803
.4808
.4812 .4817
2.1
4821
.4826
.4830
.4834
4838
.4842
4846
4850
.4854
.4857
22
4861
.4864
.4868
.4871
.4875
.4878
4881
.4884
.4887
.4890
23
.4893
.4896
.4898
.4901
4904
.4906
4909
.4911
.4913
.4916
2.4
.4918
.4920
.4922
.4925
4927
.4929
4931
.4932
.4934
.4936
2.5
4938
.4940
.4941
.4943
4945
.4946
4948
.4949
.4951
.4952
2.6
4953
.4955
.4956
.4957
4959
.4960
.4961
.4962
.4963
.4964
2.7
4965
.4966
.4967
.4968
4969
.4970
4971
4972
.4973
.4974
2.8
.4974
.4975
.4976
.4977
4977
.4978
4979
.4979
.4980
.4981
2.9
.4981
.4982
.4982
.4983
4984
.4984
.4985
.4985
.4986
.4986
3.0
.4987
.4987
.4987
.4988
4988
.4989
.4989
.4989
.4990
.4990
For values of z above 3.09, use 0.4999
en +
Transcribed Image Text:Table I: Table of Areas under the Normal Curve 06| .00 .01 .02 .03 .04 .05 .07 .08 .09 0.0 .0000 .0040 .00so .0120 .0150 .0199 .0239 .0279 .0319 .0359 0.1 .0398 .0438 .0478 .0517 .0557 .0596 .0636 .0675 .0714 .0754 0.2 .0793 .0832 .0871 .0910 .0948 .0987 1026 .1064 .1103.1141 0.3 .1179 .1217 .1253 .1293 .1331 .1368 .1406 .1443 .1480 .1517 0.4 .1554 .1591 .1628 .1664 .1700 .1736 .1772 .1808 .1844 .1879 0.5 .1915 .1950 .1985 .2019 .2054 .2088 .2123 .2157 .2190 .2224 0.6 .2258 .2291 .2324 .2357 2389 .2422 .2454 2486 .2518 .2549 0.7 2580 .2612 .2642 .2673 .2704 .2734 .2764 .2794 .2823 .2852 0.8 2881 .2910 .2939 .2967 2996 .3023 3051 .3078 .3106 .3133 0.9 3159 .3186 .3212 3288 3264 .3289 .3315 .3340 .3365 3389 1.0 3413 .3438 .3461 .3485 .3508 .3531 .3554 .3557 .3559 .3621 .3810 .3830 .3997 4015 1.1 .3642 .3665 .3686 .3708 .3729 .3749 .3770 .3790 1.2 .3849 .3869 .3888 .3907 .3925 .3944 .3962 .3980 1.3 4032 .4049 .4066 .4082 4099 .4115 4131 .4147 .4162 .4177 1.4 4192 .4207 .4222 4236 4251 .4265 4279 .4292 .4306 .4319 1.5 .4332 .4345 .4357 .4370 4382 .4394 .4406 .4418 .4429 .4441 1.6 .4452 .4463 .4474 .4484 4495 .4505 4515 4525 .4535 .4545 1.7 4554 .4564 .4573 .4582 4591 .4599 .4608 .4616 .4625 .4633 1.8 4641 .4649 .4656 4664 4671 .4678 4686 .4693 .4699 4706 1.9 4713 .4719 .4726 .4732 4738 .4744 .4750 .4756 .4761 .4767 2.0 4772 .4778 .4783 .4788 .4793 .4798 4803 .4808 .4812 .4817 2.1 4821 .4826 .4830 .4834 4838 .4842 4846 4850 .4854 .4857 22 4861 .4864 .4868 .4871 .4875 .4878 4881 .4884 .4887 .4890 23 .4893 .4896 .4898 .4901 4904 .4906 4909 .4911 .4913 .4916 2.4 .4918 .4920 .4922 .4925 4927 .4929 4931 .4932 .4934 .4936 2.5 4938 .4940 .4941 .4943 4945 .4946 4948 .4949 .4951 .4952 2.6 4953 .4955 .4956 .4957 4959 .4960 .4961 .4962 .4963 .4964 2.7 4965 .4966 .4967 .4968 4969 .4970 4971 4972 .4973 .4974 2.8 .4974 .4975 .4976 .4977 4977 .4978 4979 .4979 .4980 .4981 2.9 .4981 .4982 .4982 .4983 4984 .4984 .4985 .4985 .4986 .4986 3.0 .4987 .4987 .4987 .4988 4988 .4989 .4989 .4989 .4990 .4990 For values of z above 3.09, use 0.4999 en +
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