of obtaining a sample mean of 68 or less from a sample of 35?

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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Question
Consider a population of 300 with a mean of 65 and a standard deviation equal to 24. What is the probability of obtaining a sample mean of 68 or less from a sample of 35? (Round to four decimal places)
Cumulative probabilities for POSITIVE z-values are shown in the following table:
0.01
0.03
0.02
0.5040 0.5080 0.5120
0.5478 0.5517
Z
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2.0
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9
3.0
3.1
3.2
80%
3.3
3.4
0.00
0.5000
0.5398 0.5438
0.5793 0.5832
0.6179
0.6217
0.6554 0.6591
0.5871
0.6255
0.6628
0.9332 0.9345
0.9452
0.9463
0.9554 0.9564
0.9641 0.9649
0.9713 0.9719
0.6915 0.6950
0.6985 0.7019 0.7054
0.7257 0.7291 0.7324 0.7357 0.7389
0.7580 0.7611 0.7642 0.7673 0.7704
0.7881 0.7910 0.7939 0.7967 0.7995
0.8159 0.8186 0.8212 0.8238 0.8264
0.9772 0.9778
0.9821 0.9826
0.9861 0.9864
0.9893 0.9896
0.9918 0.9920
0.5910
0.5948
0.6293 0.6331
0.6664
0.6700
0.8413 0.8438 0.8461 0.8485 0.8508
0.8643 0.8665 0.8686 0.8708 0.8729
0.8849 0.8869 0.8888 0.8907 0.8925 0.8944
0.9032 0.9049 0.9066 0.9082 0.9099 0.9115
0.9192 0.9207
0.9236 0.9251 0.9265
0.9222
0.9357
0.9474
0.9573 0.9582
0.9656
0.9726
0.04
0.05
0.5160 0.5199
0.5557
0.5596
0.9370
0.9484
m
w
0.9938 0.9940 0.9941 0.9943 0.9945
0.9953 0.9955 0.9956 0.9957 0.9959
0.9965 0.9966 0.9967 0.9968 0.9969
0.9974 0.9975 0.9976 0.9977 0.9977
0.9981 0.9982 0.9982 0.9983 0.9984
0.9987 0.9987 0.9987 0.9988
0.9990 0.9991 0.9991 0.9991
0.9993 0.9993 0.9994 0.9994
0.9995 0.9995 0.9995 0.9996
0.9997 0.9997
0.9997 0.9997
0.07
0.08
0.5279 0.5319
0.5675 0.5714
0.5987
0.6026 0.6064 0.6103
0.6368
0.6406
0.6443 0.6480
0.6736 0.6772
0.6808 0.6844
0.06
0.5239
0.5636
0.7088 0.7123 0.7157 0.7190
0.7454
0.7486
0.7517
0.7422
0.7734
0.8023
0.8289
0.7764 0.7794 0.7823
0.8051 0.8078
0.8106
0.8315
0.8340
0.8365
0.8531 0.8554 0.8577
0.8749
0.8770 0.8790
0.9382 0.9394
0.9406
0.9418
0.9495
0.9505 0.9515
0.9525
0.9616 0.9625
0.9591 0.9599 0.9608
0.9664 0.9671 0.9678 0.9686
0.9732 0.9738 0.9744 0.9750 0.9756
0.9693
0.9699
0.9761
0.9783 0.9788 0.9793 0.9798
0.9830 0.9834 0.9838 0.9842 0.9846
0.9868 0.9871 0.9875
0.9878 0.9881
0.9898 0.9901 0.9904 0.9906 0.9909
0.9922 0.9925
0.9927
0.9929
0.9931
0.8962
0.9131
0.9279
O
0.9946
0.9948
0.9960 0.9961
0.9970 0.9971
0.9978 0.9979
0.9984 0.9985
0.9803 0.9808
0.9988 0.9989
0.9989
0.9992
0.9994
0.9996 0.9996 0.9996
0.9992 0.9992
0.9994 0.9994
0.9997
0.9997
0.9997
0.9429
0.9535
0.8599
0.8621
0.8810 0.8830
0.8980
0.8997
0.9147 0.9162
0.9292 0.9306
0.9949 0.9951
0.9962 0.9963
0.9972 0.9973
0.09
0.5359
0.5753
0.9979 0.9980
0.9985
0.9986
0.6141
0.6517
0.6879
0.9989 0.9990
0.9992 0.9993
0.9995
0.9995
0.9996
0.9996
0.9997
0.9997
0.7224
0.7549
0.7852
0.8133
0.8389
0.9812
0.9817
0.9850 0.9854
0.9857
0.9884 0.9887 0.9890
0.9911 0.9913
0.9916
0.9932
0.9934
0.9936
0.9015
0.9177
0.9319
0.9441
0.9545
0.9633
0.9706
0.9767
0.9952
0.9964
0.9974
0.9981
0.9986
0.9990
0.9993
0.9995
0.9997
0.9998
Transcribed Image Text:Cumulative probabilities for POSITIVE z-values are shown in the following table: 0.01 0.03 0.02 0.5040 0.5080 0.5120 0.5478 0.5517 Z 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0 3.1 3.2 80% 3.3 3.4 0.00 0.5000 0.5398 0.5438 0.5793 0.5832 0.6179 0.6217 0.6554 0.6591 0.5871 0.6255 0.6628 0.9332 0.9345 0.9452 0.9463 0.9554 0.9564 0.9641 0.9649 0.9713 0.9719 0.6915 0.6950 0.6985 0.7019 0.7054 0.7257 0.7291 0.7324 0.7357 0.7389 0.7580 0.7611 0.7642 0.7673 0.7704 0.7881 0.7910 0.7939 0.7967 0.7995 0.8159 0.8186 0.8212 0.8238 0.8264 0.9772 0.9778 0.9821 0.9826 0.9861 0.9864 0.9893 0.9896 0.9918 0.9920 0.5910 0.5948 0.6293 0.6331 0.6664 0.6700 0.8413 0.8438 0.8461 0.8485 0.8508 0.8643 0.8665 0.8686 0.8708 0.8729 0.8849 0.8869 0.8888 0.8907 0.8925 0.8944 0.9032 0.9049 0.9066 0.9082 0.9099 0.9115 0.9192 0.9207 0.9236 0.9251 0.9265 0.9222 0.9357 0.9474 0.9573 0.9582 0.9656 0.9726 0.04 0.05 0.5160 0.5199 0.5557 0.5596 0.9370 0.9484 m w 0.9938 0.9940 0.9941 0.9943 0.9945 0.9953 0.9955 0.9956 0.9957 0.9959 0.9965 0.9966 0.9967 0.9968 0.9969 0.9974 0.9975 0.9976 0.9977 0.9977 0.9981 0.9982 0.9982 0.9983 0.9984 0.9987 0.9987 0.9987 0.9988 0.9990 0.9991 0.9991 0.9991 0.9993 0.9993 0.9994 0.9994 0.9995 0.9995 0.9995 0.9996 0.9997 0.9997 0.9997 0.9997 0.07 0.08 0.5279 0.5319 0.5675 0.5714 0.5987 0.6026 0.6064 0.6103 0.6368 0.6406 0.6443 0.6480 0.6736 0.6772 0.6808 0.6844 0.06 0.5239 0.5636 0.7088 0.7123 0.7157 0.7190 0.7454 0.7486 0.7517 0.7422 0.7734 0.8023 0.8289 0.7764 0.7794 0.7823 0.8051 0.8078 0.8106 0.8315 0.8340 0.8365 0.8531 0.8554 0.8577 0.8749 0.8770 0.8790 0.9382 0.9394 0.9406 0.9418 0.9495 0.9505 0.9515 0.9525 0.9616 0.9625 0.9591 0.9599 0.9608 0.9664 0.9671 0.9678 0.9686 0.9732 0.9738 0.9744 0.9750 0.9756 0.9693 0.9699 0.9761 0.9783 0.9788 0.9793 0.9798 0.9830 0.9834 0.9838 0.9842 0.9846 0.9868 0.9871 0.9875 0.9878 0.9881 0.9898 0.9901 0.9904 0.9906 0.9909 0.9922 0.9925 0.9927 0.9929 0.9931 0.8962 0.9131 0.9279 O 0.9946 0.9948 0.9960 0.9961 0.9970 0.9971 0.9978 0.9979 0.9984 0.9985 0.9803 0.9808 0.9988 0.9989 0.9989 0.9992 0.9994 0.9996 0.9996 0.9996 0.9992 0.9992 0.9994 0.9994 0.9997 0.9997 0.9997 0.9429 0.9535 0.8599 0.8621 0.8810 0.8830 0.8980 0.8997 0.9147 0.9162 0.9292 0.9306 0.9949 0.9951 0.9962 0.9963 0.9972 0.9973 0.09 0.5359 0.5753 0.9979 0.9980 0.9985 0.9986 0.6141 0.6517 0.6879 0.9989 0.9990 0.9992 0.9993 0.9995 0.9995 0.9996 0.9996 0.9997 0.9997 0.7224 0.7549 0.7852 0.8133 0.8389 0.9812 0.9817 0.9850 0.9854 0.9857 0.9884 0.9887 0.9890 0.9911 0.9913 0.9916 0.9932 0.9934 0.9936 0.9015 0.9177 0.9319 0.9441 0.9545 0.9633 0.9706 0.9767 0.9952 0.9964 0.9974 0.9981 0.9986 0.9990 0.9993 0.9995 0.9997 0.9998
Cumulative probabilities for NEGATIVE z-values are shown in the following table:
Z
-3.4
-3.3
-3.2
-3.1
-3.0
-2.9
-2.8
-2.7
-2.6
-2.5
-2.4
-2.3
-2.2
-2.1
-2.0
-1.9
-1.8
-1.7
-1.6
-1.5
-1.4
-1.3
-1.2
-1.1
-1.0
-0.9
-0.8
-0.7
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0.0
0.00
0.01
0.02
0.03
0.0003 0.0003 0.0003 0.0003
0.0005 0.0005 0.0005 0.0004 0.0004
0.0007 0.0007 0.0006 0.0006
0.0006
0.0010 0.0009 0.0009 0.0009 0.0008
0.0013 0.0013 0.0013 0.0012 0.0012
0.0019 0.0018 0.0018
0.0026 0.0025 0.0024
0.0035 0.0034 0.0033
0.0047 0.0045 0.0044
0.0062 0.0060
0.0059 0.0057 0.0055
0.04
0.05
0.0003 0.0003
0.0808
0.0968
0.1151 0.1131 0.1112
0.1357 0.1335 0.1314
0.1587 0.1562 0.1539
0.0793 0.0778 0.0764
0.0951 0.0934 0.0918
0.1093
0.0287 0.0281 0.0274 0.0268 0.0262 0.0256
0.0359 0.0351 0.0344 0.0336 0.0329 0.0322
0.0446 0.0436 0.0427 0.0418 0.0409 0.0401
0.0548 0.0537 0.0526 0.0516 0.0505 0.0495
0.0668 0.0655 0.0643 0.0630 0.0618 0.0606
0.0004 0.0004
HH
0.0006 0.0006
0.0008
0.0008
0.0011
0.0011
0.0017 0.0016 0.0016 0.0015 0.0015 0.0014
0.0023 € 0.0023 0.0022 0.0021 0.0021 0.0020
0.0032 0.0031 0.0030 0.0029 0.0028 0.0027
0.0043 0.0041 0.0040 0.0039 0.0038 0.0037
0.0054
¹0.0052 0.0051
0.0049
0.0071
0.0069
0.0068
0.0066
0.0091 0.0089
0.0087
0.0113
0.0082 0.0080 0.0078 0.0075 0.0073
0.0107 0.0104 0.0102 0.0099 0.0096 0.0094
0.0139 0.0136 0.0132 0.0129 0.0125 0.0122 0.0119 0.0116
0.0179 0.0174 0.0170 0.0166 0.0162 0.0158 0.0154 0.0150 0.0146
0.0228 0.0222 0.0217 0.0212 0.0207 0.0202 0.0197 0.0192 0.0188
0.06
0.07
0.0003 0.0003
0.1292
0.1271
0.1515 0.1492
0.1841 0.1814
0.1788 0.1762
0.2119 0.2090 0.2061
0.2420 0.2389 0.2358
0.1736 0.1711
0.2033 0.2005 0.1977
0.2327
0.2743 0.2709 0.2676 0.2643
0.3085 0.3050 0.3015 0.2981
0.08
0.0003
0.0004 0.0004
0.0005 0.0005
0.0008 0.0007
0.0011 0.0010
0.0749 0.0735 0.0721 0.0708
0.0869 0.0853
0.0901
0.0885
0.1075
0.1056
0.1038 0.1020
0.1251
0.1469
0.0250 0.0244 0.0239
0.0314 0.0307 0.0301
0.0392 0.0384 0.0375
0.0485 0.0475 0.0465
0.0594 0.0582
O
0.3446
0.3264
0.3632
0.3409 0.3372 0.3336 0.3300
0.3821 0.3783 0.3745 0.3707 0.3669
0.4207 0.4168 0.4129 0.4090 0.4052 0.4013 0.3974
0.4602 0.4562 0.4522 0.4483 0.4443 0.4404 0.4364
0.4920 0.4880 0.4840 0.4801
0.5000 0.4960
0.4761
0.0694
0.0838
0.1003
0.1230 0.1210 0.1190
0.1446
0.1423 0.1401
0.1685
0.1660 0.1635
0.1894
0.1949 0.1922
0.2296 0.2266 0.2236 0.2206 0.2177
0.2611 0.2578 0.2546 0.2514 0.2483
0.2946 0.2912 0.2877
0.2843
0.2810
0.3192 0.3156
0.3228
0.3594 0.3557 0.3520
0.09
0.0002
0.0003
0.0005
0.0007
0.0010
0.0014
0.0019
0.0367
0.0455
0.0571 0.0559
0.4325 0.4286
0.4721
0.4681
0.0026
0.0036
0.0048
0.0064
0.0084
0.0110
0.0143
0.0183
0.0233
0.0294
0.0681
0.0823
0.0985
0.1170
0.1379
0.1611
0.1867
0.2148
0.2451
0.2776
0.3121
0.3483
0.3936 0.3897 0.3859
0.4247
0.4641
Transcribed Image Text:Cumulative probabilities for NEGATIVE z-values are shown in the following table: Z -3.4 -3.3 -3.2 -3.1 -3.0 -2.9 -2.8 -2.7 -2.6 -2.5 -2.4 -2.3 -2.2 -2.1 -2.0 -1.9 -1.8 -1.7 -1.6 -1.5 -1.4 -1.3 -1.2 -1.1 -1.0 -0.9 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.00 0.01 0.02 0.03 0.0003 0.0003 0.0003 0.0003 0.0005 0.0005 0.0005 0.0004 0.0004 0.0007 0.0007 0.0006 0.0006 0.0006 0.0010 0.0009 0.0009 0.0009 0.0008 0.0013 0.0013 0.0013 0.0012 0.0012 0.0019 0.0018 0.0018 0.0026 0.0025 0.0024 0.0035 0.0034 0.0033 0.0047 0.0045 0.0044 0.0062 0.0060 0.0059 0.0057 0.0055 0.04 0.05 0.0003 0.0003 0.0808 0.0968 0.1151 0.1131 0.1112 0.1357 0.1335 0.1314 0.1587 0.1562 0.1539 0.0793 0.0778 0.0764 0.0951 0.0934 0.0918 0.1093 0.0287 0.0281 0.0274 0.0268 0.0262 0.0256 0.0359 0.0351 0.0344 0.0336 0.0329 0.0322 0.0446 0.0436 0.0427 0.0418 0.0409 0.0401 0.0548 0.0537 0.0526 0.0516 0.0505 0.0495 0.0668 0.0655 0.0643 0.0630 0.0618 0.0606 0.0004 0.0004 HH 0.0006 0.0006 0.0008 0.0008 0.0011 0.0011 0.0017 0.0016 0.0016 0.0015 0.0015 0.0014 0.0023 € 0.0023 0.0022 0.0021 0.0021 0.0020 0.0032 0.0031 0.0030 0.0029 0.0028 0.0027 0.0043 0.0041 0.0040 0.0039 0.0038 0.0037 0.0054 ¹0.0052 0.0051 0.0049 0.0071 0.0069 0.0068 0.0066 0.0091 0.0089 0.0087 0.0113 0.0082 0.0080 0.0078 0.0075 0.0073 0.0107 0.0104 0.0102 0.0099 0.0096 0.0094 0.0139 0.0136 0.0132 0.0129 0.0125 0.0122 0.0119 0.0116 0.0179 0.0174 0.0170 0.0166 0.0162 0.0158 0.0154 0.0150 0.0146 0.0228 0.0222 0.0217 0.0212 0.0207 0.0202 0.0197 0.0192 0.0188 0.06 0.07 0.0003 0.0003 0.1292 0.1271 0.1515 0.1492 0.1841 0.1814 0.1788 0.1762 0.2119 0.2090 0.2061 0.2420 0.2389 0.2358 0.1736 0.1711 0.2033 0.2005 0.1977 0.2327 0.2743 0.2709 0.2676 0.2643 0.3085 0.3050 0.3015 0.2981 0.08 0.0003 0.0004 0.0004 0.0005 0.0005 0.0008 0.0007 0.0011 0.0010 0.0749 0.0735 0.0721 0.0708 0.0869 0.0853 0.0901 0.0885 0.1075 0.1056 0.1038 0.1020 0.1251 0.1469 0.0250 0.0244 0.0239 0.0314 0.0307 0.0301 0.0392 0.0384 0.0375 0.0485 0.0475 0.0465 0.0594 0.0582 O 0.3446 0.3264 0.3632 0.3409 0.3372 0.3336 0.3300 0.3821 0.3783 0.3745 0.3707 0.3669 0.4207 0.4168 0.4129 0.4090 0.4052 0.4013 0.3974 0.4602 0.4562 0.4522 0.4483 0.4443 0.4404 0.4364 0.4920 0.4880 0.4840 0.4801 0.5000 0.4960 0.4761 0.0694 0.0838 0.1003 0.1230 0.1210 0.1190 0.1446 0.1423 0.1401 0.1685 0.1660 0.1635 0.1894 0.1949 0.1922 0.2296 0.2266 0.2236 0.2206 0.2177 0.2611 0.2578 0.2546 0.2514 0.2483 0.2946 0.2912 0.2877 0.2843 0.2810 0.3192 0.3156 0.3228 0.3594 0.3557 0.3520 0.09 0.0002 0.0003 0.0005 0.0007 0.0010 0.0014 0.0019 0.0367 0.0455 0.0571 0.0559 0.4325 0.4286 0.4721 0.4681 0.0026 0.0036 0.0048 0.0064 0.0084 0.0110 0.0143 0.0183 0.0233 0.0294 0.0681 0.0823 0.0985 0.1170 0.1379 0.1611 0.1867 0.2148 0.2451 0.2776 0.3121 0.3483 0.3936 0.3897 0.3859 0.4247 0.4641
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