What percent of IQ scores are less than 122? B. What is the probability that a randomly selected adult in this age group has an IQ score higher than 147? Is this a significant/unusual event? Explain. C. What percent of adults in this age group have  IQs between 85 and 100? Is this significant/unusual event? Explain.

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Scores on the Wechsler Adult intelligence Scale (a standard ID test) for certain age group are normally distributed with mean μ = 100 and standard deviation σ = 15.  (Find the Z score/s for each question first, and then use Table A-2 at the back of your book to find the following probabilities).

A. What percent of IQ scores are less than 122?

B. What is the probability that a randomly selected adult in this age group has an IQ score higher than 147? Is this a significant/unusual event? Explain.

C. What percent of adults in this age group have  IQs between 85 and 100? Is this significant/unusual event? Explain.

NEGATIVE z Scores
TABLE A-2 Standard Normal (z) Distribution: Cumulative Area from the LEFT
.00
.01
.02
.03
.04
.05
.06
.07
.08
.09
-3.50 and
lower
.0001
-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
.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
NOTE: For values of z below –3.49, use 0.0001 for the area.
(continued)
*Use these common values that result from interpolation:
z Score
Area
-1.645
0.0500
-2.575
0.0050
N
Transcribed Image Text:NEGATIVE z Scores TABLE A-2 Standard Normal (z) Distribution: Cumulative Area from the LEFT .00 .01 .02 .03 .04 .05 .06 .07 .08 .09 -3.50 and lower .0001 -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 .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 NOTE: For values of z below –3.49, use 0.0001 for the area. (continued) *Use these common values that result from interpolation: z Score Area -1.645 0.0500 -2.575 0.0050 N
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