Given a normal random variable X with mean 68 and variance 25, and a random sample of size n taken from the distribution, what sample size n is necessary in order that P(67.8sXs68.2)=0.97? Click here to view page 1 of the standard normal distribution table. Click here to view page 2 of the standard normal distribution table. The necessary sample size is n = (Round up to the nearest whole number.)
Given a normal random variable X with mean 68 and variance 25, and a random sample of size n taken from the distribution, what sample size n is necessary in order that P(67.8sXs68.2)=0.97? Click here to view page 1 of the standard normal distribution table. Click here to view page 2 of the standard normal distribution table. The necessary sample size is n = (Round up to the nearest whole number.)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Transcribed Image Text:Areas under the Normal Curve
[=
Areas under the Normal Curve
z
-2.9 0.0019 0.0018 0.0018 0.0017
-2.8
0.0026 0.0025 0.0024
0.0023 0.0023
-2.7
0.0035 0.0034 0.0033
0.0032
-0.5
0.3050
0.3015
0.2981
-0.4
0.3446 0.3409
0.3372
0.3336
-0.3
0.3821
0.3783
0.3745
0.3707
0.3669
-0.2
0.4207
0.4168
0.4129
0.4090
0.4052
-0.1
0.4602
0.4562
0.4522 0.4483 0.4443
.00
.01
.02
.03
.04
.05
.06
-3.4 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003
-3.3 0.0005 0.0005 0.0005 0.0004 0.0004 0.0004 0.0004
0.0007
-3.2
0.0006
0.0007
0.0006
0.0006 0.0006 0.0006
-3.1 0.0010 0.0009 0.0009
0.0008
0.0009 0.0008 0.0008
-3.0 0.0013 0.0013 0.0013 0.0012 0.0012 0.0011 0.0011
0.0016 0.0016 0.0015
0.0022 0.0021
0.0029
0.0031
0.0030
-2.6 0.0047 0.0045 0.0044 0.0043 0.0041 0.0040 0.0039
-2.5 0.0062 0.0060 0.0059 0.0057 0.0055 0.0054 0.0052
-2.4
0.0080 0.0078
0.0082
0.0075 0.0073 0.0071 0.0069
-2.3 0.0107
0.0102 0.0099
0.0104
0.0096
0.0091
0.0094
-2.2 0.0139 0.0136 0.0132 0.0129 0.0125
0.0122 0.0119
0.0179 0.0174 0.0170 0.0166 0.0162
-2.1
0.0158 0.0154
0.0228
-2.0
0.0222 0.0217 0.0212
0.0197
0.0207 0.0202
-1.9
0.0281
0.0287
0.0268 0.0262 0.0256
0.0274
0.0359
-1.8
0.0351 0.0344 0.0336
0.0322
0.0329
-1.7 0.0446 0.0436 0.0427 0.0418 0.0409 0.0401
0.0384
0.0392
-1.6
0.0537 0.0526 0.0516
0.0548
0.0505 0.0495 0.0485 0.0475
-1.5 0.0668 0.0655 0.0643 0.0630 0.0618 0.0606 0.0594 0.0582
-1.4 0.0808 0.0793 0.0778
0.0735
0.0764
0.0721
0.0749
0.0708
-1.3 0.0968 0.0951 0.0934 0.0918 0.0901 0.0885 0.0869 0.0853
-1.2 0.1151 0.1131
0.1093 0.1075
0.1112
0.1020
0.1056 0.1038
-1.1 0.1357 0.1335 0.1314 0.1292 0.1271 0.1251 0.1230 0.1210
0.1587 0.1562 0.1539
0.1469
-1.0
0.1423
0.1515 0.1492
0.1446
0.1841 0.1814
0.1762
-0.9
0.1736 0.1711 0.1685
0.1788
0.1660
-0.8 0.2119 0.2090 0.2061 0.2033 0.2005 0.1977 0.1949 0.1922
-0.7 0.2420 0.2389 0.2358 0.2327 0.2296 0.2266 0.2236 0.2206
-0.6 0.2743 0.2709 0.2676 0.2643 0.2611
0.2546 0.2514
0.2578
0.3085
0.2912
0.2946
0.2877 0.2843 0.2810 0.2776 -0.5
0.3228 0.3192
0.3156 0.3121 -0.4
0.3483
0.3557 0.3520
0.3936 0.3897 0.3859
0.4325 0.4286 0.4247
.08
.07
0.0003 0.0003 0.0002 -3.4
0.0004 0.0004 0.0003 -3.3
0.0005
0.0005 0.0005
-3.2
0.0008 0.0007 0.0007 -3.1
0.0011 0.0010 0.0010 -3.0
.09
之
0.2
0.3
0.5793
0.6179
0.0015 0.0014 0.0014 -2.9
0.0020
0.0019 -2.8
0.0021
0.0028 0.0027 0.0026 -2.7
0.0038 0.0037 0.0036
-2.6
0.0051 0.0049 0.0048 -2.5
0.0068 0.0066
0.0089 0.0087
0.0116 0.0113
0.0146
0.0150
0.0192 0.0188
0.6
0.7
0.8
1.0
0.0064 -2.4
0.0084
0.0110 -2.2
0.0143 -2.1
0.0183
-2.3
1.1
1.2
1.3
0.9032
1.4
-2.0
0.0250
0.0244
0.0314
0.0307
0.0239 0.0233
0.0301 0.0294
0.0375 0.0367 -1.7
0.0465
-1.6
0.0455
0.0571 0.0559 -1.5
-1.4
0.0694 0.0681
0.0838 0.0823 -1.3
-1.2
0.1003 0.0985
0.1190 0.1170 -1.1
0.1401
-1.0
0.1379
0.1635 0.1611 -0.9
0.1894 0.1867 -0.8
0.2177 0.2148
-0.7
0.2483 0.2451 -0.6
-1.9
1.5
-1.8
2.0
0.9861
0.9871
田
0.3300 0.3264
0.3632
0.3594
-0.3
0.4013
0.3974
-0.2
C
0.4404
0.4364
-0.1
-0.0
0.5000
.00
0.4960
.01
0.4920 0.4880 0.4840
.02
.03
.04
0.4801
.05
0.4761
.06
0.4721 0.4681 0.4641 -0.0 ¡Ai
.07
.08
.09
-->0 (
1
0.9991
0.9993
3.3
0.9995
3.4
0.9997
2
.00
.01
.02
.03
.04
z
.00
.01
.02
.03
.04
.05
.06
0.0 0.5000 0.5040 0.5080 0.5120 0.5160 0.5199 0.5239 0.5279 0.5319 0.5359 0.0
0.1 0.5398 0.5438 0.5478 0.5517 0.5557
0.5596 0.5636 0.5675 0.5714 0.5753 0.1
0.5832
0.6103
0.6064
0.6141 0.2
0.5871 0.5910 0.5948 0.5987 0.6026
0.6293
0.3
0.6217 0.6255
0.6331 0.6368 0.6406 0.6443 0.6480 0.6517
0.4 0.6554 0.6591
0.6628 0.6664 0.6700 0.6736 0.6772 0.6808 0.6844 0.6879 0.4
0.5 0.6915 0.6950 0.6985 0.7019 0.7054 0.7088 0.7123 0.7157 0.7190 0.7224 0.5
0.7291
0.7257
0.7357
0.7324
0.7422
0.7389
0.7454
0.7517
0.7486
0.7549 0.6
0.7580
0.7642
0.7611
0.7704
0.7673
0.7734 0.7764 0.7794 0.7823 0.7852
0.7881 0.7910 0.7939 0.7967 0.7995 0.8023 0.8051 0.8078 0.8106 0.8133 0.8
0.9 0.8159 0.8186 0.8212 0.8238 0.8264
0.8289 0.8315 0.8340 0.8365 0.8389 0.9
0.8413 0.8438 0.8461 0.8485 0.8508 0.8531 0.8554 0.8577 0.8599 0.8621 1.0
0.8708
0.8643 0.8665 0.8686
0.8729 0.8749
0.8830
0.8770 0.8790 0.8810
1.1
0.8888
0.8849 0.8869
0.8907 0.8925 0.8944 0.8962 0.8980 0.8997 0.9015 1.2
0.9049 0.9066
0.9099 0.9115
0.9162 0.9177
0.9082
0.9131 0.9147
1.3
0.9306
0.9192
0.9207 0.9222 0.9236 0.9251 0.9265 0.9279 0.9292
1.4
0.9332
0.9406
0.9345 0.9357 0.9370 0.9382
0.9394
0.9429
0.9418
1.5
1.6 0.9452 0.9463
0.9535
0.9474 0.9484
1.6
0.9495 0.9505 0.9515 0.9525
0.9545
1.7 0.9554 0.9564 0.9573 0.9582 0.9591 0.9599
0.9616
0.9608
0.9625 0.9633 1.7
1.8 0.9641 0.9649
0.9693
0.9656 0.9664 0.9671 0.9678 0.9686
0.9706 1.8
0.9699
1.9 0.9713 0.9719 0.9726 0.9732 0.9738 0.9744 0.9750 0.9756 0.9761 0.9767 1.9
0.9778 0.9783
0.9772
0.9788
0.9803
0.9793
0.9817 2.0
0.9812
0.9798
0.9808
2.1 0.9821 0.9826 0.9830 0.9834 0.9838 0.9842 0.9846 0.9850 0.9854 0.9857 2.1
2.2
0.9864
0.9868
0.9875
0.9881 0.9884 0.9887 0.9890
2.3 0.9893 0.9896 0.9898 0.9901 0.9904 0.9906 0.9909 0.9911 0.9913 0.9916 2.3
2.4
0.9920
0.9925
0.9918
0.9922
0.9934
0.9927
2.4
0.9929 0.9931 0.9932
0.9936
2.5 0.9938
0.9941 0.9943
0.9948
0.9951
2.5
0.9940
0.9945 0.9946
0.9949
0.9952
2.6 0.9953 0.9955 0.9956 0.9957 0.9959 0.9960 0.9961 0.9962 0.9963 0.9964 2.6
0.9965
0.9967
0.9969 0.9970
0.9973
0.9974
2.7
0.9966
0.9968
0.9971
0.9972
2.7
0.9977 0.9977
2.8 0.9974 0.9975
0.9976
0.9978 0.9979 0.9979 0.9980 0.9981 2.8
2.9 0.9981 0.9982
0.9983 0.9984
0.9982
0.9985 0.9985
0.9984
0.9986 0.9986 2.9
3.0 0.9987 0.9987 0.9987 0.9988 0.9988 0.9989 0.9989 0.9989 0.9990 0.9990 3.0
3.1 0.9990
0.9991
0.9992 0.9992
0.9992 0.9993
0.9991
0.9993
0.9992
3.2
0.9994
0.9993
0.9995
0.9994 0.9994 0.9994 0.9994 0.9995
0.9995
0.9995 0.9996
0.9995
0.9996
0.9996
0.9996 0.9996 0.9996 0.9997
0.9997 0.9997 0.9997 0.9997
0.9997
0.9997
0.9997
0.9997
0.9998
.05
.06
.07
.08
.09
.07
.08
.09
名
0.7
0.9319
0.9441
0.9878
2.2
3.1
3.2
3.3
3.4
Transcribed Image Text:Given a normal random variable X with mean 68 and variance 25, and a random sample of size n taken from the distribution, what sample size n is
necessary in order that P(67.8≤x≤68.2) = 0.97?
Click here to view page 1 of the standard normal distribution table.
Click here to view page 2 of the standard normal distribution table.
The necessary sample size is n =
(Round up to the nearest whole number.)
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