Use Table A to find the value z of a standard Normal variable that satisfies each of the following conditions. Use the value of z from Table A that comes closest to satisfying the condition. In each case, sketch a standard Normal curve with your value of z marked on the axis. (a) Find the point z with 66% of the observations falling below it. Enter your answer rounded to two decimal places. z= (b) Find the point z with 24% of the observations falling above it. Enter your answer rounded to two decimal places. z=
Use Table A to find the value z of a standard Normal variable that satisfies each of the following conditions. Use the value of z from Table A that comes closest to satisfying the condition. In each case, sketch a standard Normal curve with your value of z marked on the axis. (a) Find the point z with 66% of the observations falling below it. Enter your answer rounded to two decimal places. z= (b) Find the point z with 24% of the observations falling above it. Enter your answer rounded to two decimal places. z=
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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Normal Distribution
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Question
Use Table A to find the value z of a standard Normal variable that satisfies each of the following conditions. Use the value of z from Table A that comes closest to satisfying the condition. In each case, sketch a standard Normal curve with your value of z marked on the axis.
(a) Find the point z with 66% of the observations falling below it. Enter your answer rounded to two decimal places.
z=
(b) Find the point z with 24% of the observations falling above it. Enter your answer rounded to two decimal places.
z=
Transcribed Image Text:696
TABLES
Table entry for z is the area under the
Table entry
standard Normal curve to the left of z.
TABLE A Standard normal cumulative proportions
.00
.01
.02
.03
.04
.05
.06
.07
.08
.09
-3.4
.0003
.0003
.0003
.0003
.0003
.0003
.0003
.0003
.0003
.0002
.0003
.0005
.0007
.0005
.0004
.0006
-3.3
.0005
.0005
.0004
.0004
.0004
.0004
.0004
-3.2
.0007
.0007
.0006
.0006
.0006
.0006
.0005
.0005
-3.1
.0010
.0009
.0009
.0009
.0008
.0008
.0008
.0008
.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
.0023
.0032
-2.8
.0026
.0025
.0024
.0023
.0022
.0021
.0021
.0020
.0019
-2.7
.0035
.0034
.0033
.0031
.0030
.0029
.0028
.0027
.0026
-2.6
.0047
.0045
.0044
.0043
.0041
.0040
.0054
.0039
.0038
.0037
.0036
-2.5
.0062
.0060
.0059
.0057
.0055
.0052
.0051
.0049
.0048
-2.4
.0064
.0084
.0082
.0080
.0078
.0075
.0073
.0071
.0069
.0068
.0066
-2.3
.0107
.0104
.0102
.0099
.0096
.0094
.0091
.0089
.0087
-2.2
.0139
.0136
.0132
.0129
.0125
.0122
.0119
.0116
.0113
.0110
.0174
.0222
.0170
.0217
-2.1
.0179
.0166
.0162
.0158
.0154
.0150
.0146
.0143
-2.0
.0228
.0212
.0207
.0202
.0197
.0192
.0188
.0183
.0274
.0287
.0359
.0281
.0268
.0262
.0256
.0250
.0233
.0244
.0307
.0384
-1.9
.0239
.0314
- 1.8
- 1.7
.0336
.0418
.0516
.0329
.0409
.0351
.0344
.0322
.0301
.0294
.0446
.0436
.0427
.0401
.0392
.0375
.0367
.0485
.0505
.0618
.0455
.0548
.0668
-1.6
.0537
.0526
.0495
.0475
.0465
-1.5
.0655
.0643
.0630
.0606
.0594
.0582
.0571
.0559
-1.4
-1.3
.0694
.0838
.0808
.0793
.0778
.0764
.0749
.0735
.0721
.0708
.0681
.0968
.0951
.0934
.0918
.0901
.0885
.0869
.0853
.0823
- 1.2
- 1.1
.1038
.1230
.1151
.1131
.1112
.1093
.1075
.1056
.1020
.1003
.0985
.1357
.1335
.1314
.1292
.1271
.1251
.1210
.1190
.1170
-1.0
.1587
.1562
.1539
.1515
.1492
.1469
.1446
.1423
.1401
.1379
.1814
.2090
-0.9
.1841
.1788
.1762
.1736
.1711
.1685
.1660
.1635
.1611
-0.8
.2119
.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
.3409
.3783
.4168
-0.4
.3446
.3372
.3336
3300
.3264
.3228
.3192
.3156
.3121
-0.3
.3821
.3745
3707
.3669
.3632
.3594
.3557
3520
.3483
.4090
.4483
.4880
-0.2
.4207
.4129
.4052
.4013
.3974
.3936
.3897
.3859
.4404
.4801
.4247
.4641
-0.1
.4602
.4562
.4522
.4443
.4364
.4325
.4286
-0.0
.5000
.4960
.4920
.4840
.4761
.4721
.4681
Transcribed Image Text:TABLES
697
Table entry
Table entry for z is the area under the
standard Normal curve to the left of z.
TABLE A Standard Normal cumulative proportions (continued)
.00
.01
.02
.03
.04
.05
.06
.07
.08
.09
0.0
.5000
.5040
.5080
.5120
.5160
.5199
.5239
.5279
.5319
.5359
.5557
.5948
.6331
.5636
.6026
0.1
.5398
.5438
.5478
.5517
.5596
.5675
.5714
.5753
0.2
.5793
.5832
.5871
.5910
.5987
.6064
.6103
.6141
0.3
0.4
.6406
.6772
.6480
.6844
.6179
.6217
.6255
.6293
.6368
.6443
.6517
.6554
.6591
.6628
.6664
.6700
.6736
.6808
.6879
.6950
.7054
.7389
.7088
.7422
.7123
.7454
.7764
0.5
.6915
.6985
.7019
.7157
.7190
.7224
0.6
.7257
.7580
.7517
.7823
.8106
.7291
.7324
.7357
.7486
.7794
.8078
.8340
.7549
0.7
.7611
.7642
.7673
.7704
.7734
.7852
.8023
.8289
0.8
.7881
.7910
.7939
.7967
.7995
.8051
.8133
0.9
.8159
.8186
.8212
.8238
.8264
.8315
.8365
.8389
.8485
.8708
.8907
.8508
.8577
.8790
1.0
.8413
.8438
.8461
.8531
.8554
.8599
.8621
.8643
.8849
.8749
.8944
1.1
.8665
.8686
.8729
.8770
.8810
.8830
1.2
.8869
.8888
.8925
.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
.9463
.9564
1.6
.9452
.9474
.9484
.9495
.9505
.9515
.9525
.9535
.9545
1.7
.9554
.9573
.9582
.9591
.9599
.9608
.9616
.9625
.9633
.9678
.9744
1.8
.9641
.9649
.9656
.9664
.9671
.9686
.9693
.9699
.9706
1.9
.9713
.9719
.9726
.9732
.9738
.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
.9887
.9913
.9857
2.2
.9861
.9864
.9868
.9871
.9875
.9878
.9881
.9884
.9890
2.3
.9893
.9896
.9898
.9901
.9904
.9906
.9909
.9911
.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
.9977
.9983
2.8
.9974
.9975
.9976
.9977
.9978
.9979
.9979
.9980
.9981
2.9
.9981
.9982
.9982
.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
.9996
.9995
.9995
.9995
3.3
.9995
.9995
.9995
.9996
.9996
.9996
.9996
.9996
.9997
3.4
.9997
.9997
.9997
.9997
.9997
.9997
.9997
.9997
.9997
.9998
Expert Solution
Step 1
a)
The point z with 66% of the observations falling below it is obtained as below:
The value of z is obtained as follows:
The value of z is obtained from Excel using "=NORMSINV(probability)".
Output obtained using Excel is given below:
From the output, the z value is 0.41.
Thus, the point z with 66% of the observations falling below it is 0.41.
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