Q2. [6 points] Ages in a data set can be shown to be normally distributed with a mean of 50 years and a standard deviation of 6 years. A powerful individual is randomly selected from the data and his age is observed (1) Find the probability that his age will fall between 55 and 60 years (i1)Find the probability that his age will be less than 35 years, Find the value ofK such that P(X>K)=0.44 (iii)

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
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Q2. [6 points] Ages in a data set can be shown to be normally distributed with a mean of 50 years
and a standard deviation of 6 years. A powerful individual is randomly selected from the data and
his age is observed
(1) Find the probability that his age will fall between 55 and 60 years
(ii)Find the probability that his age will be less than 35 years,
Find the value of K such that P(X>K)=0.44
(ii)
00
.01
.02
.03
.04
os
.06
07
OB
09
0000
0040
OO80
0120
0160
0199
0239
0279
0359
O198
0438
0478
.0517
OS57
0596
06 36
0675
0714
0753
0793
O832
0871
0910
0948
.0987
.1026
1064
1103
1141
1255
1293
1 368
1406
1443
1480
1517
1179
1217
1331
04
1554
1591
1628
1664
1700
1736
1アアコ
1AOA
1A44
1479
1915
1950
1985
2019
2054
2088
2123
2157
2190
2224
16
2257
2291
2324
2357
2389
2422
2454
2486
2517
2549
07
2580
2611
2642
2673
2704
2734
2764
2794
2823
2852
2881
2910
2939
2967
2995
3023
3051
3078
3106
3133
3159
3186
2 ו 2ב
3238
3264
3289
3315
3340
3365
3389
10
3413
3438
3461
3465
3508
3531
3554
3577
3599
3621
3643
3665
3G86
3708
3729
3749
3770
3790
3810
3830
3669
3888
3907
3925
3944
3962
3980
3997
4015
12
3843
4037
4049
4066
4082
4099
4115
4131
4147
4162
4177
Transcribed Image Text:Q2. [6 points] Ages in a data set can be shown to be normally distributed with a mean of 50 years and a standard deviation of 6 years. A powerful individual is randomly selected from the data and his age is observed (1) Find the probability that his age will fall between 55 and 60 years (ii)Find the probability that his age will be less than 35 years, Find the value of K such that P(X>K)=0.44 (ii) 00 .01 .02 .03 .04 os .06 07 OB 09 0000 0040 OO80 0120 0160 0199 0239 0279 0359 O198 0438 0478 .0517 OS57 0596 06 36 0675 0714 0753 0793 O832 0871 0910 0948 .0987 .1026 1064 1103 1141 1255 1293 1 368 1406 1443 1480 1517 1179 1217 1331 04 1554 1591 1628 1664 1700 1736 1アアコ 1AOA 1A44 1479 1915 1950 1985 2019 2054 2088 2123 2157 2190 2224 16 2257 2291 2324 2357 2389 2422 2454 2486 2517 2549 07 2580 2611 2642 2673 2704 2734 2764 2794 2823 2852 2881 2910 2939 2967 2995 3023 3051 3078 3106 3133 3159 3186 2 ו 2ב 3238 3264 3289 3315 3340 3365 3389 10 3413 3438 3461 3465 3508 3531 3554 3577 3599 3621 3643 3665 3G86 3708 3729 3749 3770 3790 3810 3830 3669 3888 3907 3925 3944 3962 3980 3997 4015 12 3843 4037 4049 4066 4082 4099 4115 4131 4147 4162 4177
Find the value of K such that P(X>K)=0.44
.00
.01
.02
.03
.04
.0s
.06
.07
.08
.09
0.0
.0000
0040
.o080
0120
.0160
0199
.0239
.0279
.0319
.0359
0.1
.0398
.0438
.0478
.0517
.0557
.0596
.0636
0.2
.0793
.0675
.0714
.0753
0832
0871
.0910
.0948
„0987
.1026
0.3
.1179
.1217
.1064
.1103
.1141
1255
.1293
.1331
.1368
.1406
1443
0.4
1554
.1591
.1628
.1664
1480
.1517
.1760
.1736
.1772
1868
1844
.1879
0.5
1915
.1950
.1985
2019
2054
2088
2123
2157
.2190
2224
0.6
2257
2291
2324
.2357
2389
2422
2454
2486
2517
2549
0.7
2580
2611
2642
2673
2704
2734
2764
2794
2823
.2852
O.B
2881
2910
2939
2967
2995
3023
3051
3078
3106
3133
0.9
.3159
3186
3212
3238
.3264
1.0
3289
3315
3340
.3365
.3389
3413
3438
3461
.3485
3508
.3531
3554
1.1
3643
3665
.3577
.3599
3621
3686
.3708
.3729
3749
3770
1.2
3849
3869
.3790
.3810
.3830
3888
.3907
3925
3944
3962
1.3
4032
4049
3980
.3997
4015
4066
4082
4099
4131
1.4
4192
4207
4222
4236
4147
4162
4177
.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
1.7
4505
4515
4525
.4535
.4545
4554
4564
4573
4582
4591
4599
1.8
4608
4616
.4625
4633
4706
4641
A649
A656
4664
4671
AG75
.4686
19
4713
4G93
4699
4719
4726
4732
4738
4744
4750
20
4772
AT76
A783
4788
4756
4761
4767
4793
4795
4803
4808
4812
4817
21
A821
4826
4830
4834
4838
4842
4846
4850
A854
2.2
4857
4564
4896
4861
4566
4871
4875
4078
4881
4854
23
4893
4887
4890
4898
4901
4904
4906
4909
24
4918
4220
4911
4913
4916
4922
4925
4927
4229
4931
4932
25
4935
4940
4941
4945
4934
4936
4243
4346
4348
4249
4951
4352
ENG
24
6057
a
Transcribed Image Text:Find the value of K such that P(X>K)=0.44 .00 .01 .02 .03 .04 .0s .06 .07 .08 .09 0.0 .0000 0040 .o080 0120 .0160 0199 .0239 .0279 .0319 .0359 0.1 .0398 .0438 .0478 .0517 .0557 .0596 .0636 0.2 .0793 .0675 .0714 .0753 0832 0871 .0910 .0948 „0987 .1026 0.3 .1179 .1217 .1064 .1103 .1141 1255 .1293 .1331 .1368 .1406 1443 0.4 1554 .1591 .1628 .1664 1480 .1517 .1760 .1736 .1772 1868 1844 .1879 0.5 1915 .1950 .1985 2019 2054 2088 2123 2157 .2190 2224 0.6 2257 2291 2324 .2357 2389 2422 2454 2486 2517 2549 0.7 2580 2611 2642 2673 2704 2734 2764 2794 2823 .2852 O.B 2881 2910 2939 2967 2995 3023 3051 3078 3106 3133 0.9 .3159 3186 3212 3238 .3264 1.0 3289 3315 3340 .3365 .3389 3413 3438 3461 .3485 3508 .3531 3554 1.1 3643 3665 .3577 .3599 3621 3686 .3708 .3729 3749 3770 1.2 3849 3869 .3790 .3810 .3830 3888 .3907 3925 3944 3962 1.3 4032 4049 3980 .3997 4015 4066 4082 4099 4131 1.4 4192 4207 4222 4236 4147 4162 4177 .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 1.7 4505 4515 4525 .4535 .4545 4554 4564 4573 4582 4591 4599 1.8 4608 4616 .4625 4633 4706 4641 A649 A656 4664 4671 AG75 .4686 19 4713 4G93 4699 4719 4726 4732 4738 4744 4750 20 4772 AT76 A783 4788 4756 4761 4767 4793 4795 4803 4808 4812 4817 21 A821 4826 4830 4834 4838 4842 4846 4850 A854 2.2 4857 4564 4896 4861 4566 4871 4875 4078 4881 4854 23 4893 4887 4890 4898 4901 4904 4906 4909 24 4918 4220 4911 4913 4916 4922 4925 4927 4229 4931 4932 25 4935 4940 4941 4945 4934 4936 4243 4346 4348 4249 4951 4352 ENG 24 6057 a
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