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.)
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 31PPS
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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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