Question
A survey is planned to determine the mean annual family medical expenses of employees of a large company. The management of the company wishes to
A survey is planned to determine the mean annual family medical expenses of employees of a large company. The management of the company wishes to be 99% confident that the sample mean is correct to within $60 of the population mean annual family medical expenses. A previous study indicates that the standard deviation is approximately $397.
a. How large a sample isnecessary?
b. If management wants to be correct to within $20, how many employees need to beselected?
Click here to view page 1 of the cumulative standardized normal distribution table.1
Click here to view page 2 of the cumulative standardized normal distribution table.2
a. How large a sample isnecessary?
n=
(Round up to the nearestinteger.)
b. If management wants to be correct to within $20, how many employees need to beselected?
n=
(Round up to the nearestinteger.)
Cumulative Probabilities
Z
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
6.0
0.000000001
5.5
0.000000019
5.0
0.000000287
4.5
0.000003398
4.0
0.000031671
3.9
0.00005
0.00005
0.00004
0.00004
0.00004
0.00004
0.00004
0.00003
0.00003
0.00003
3.8
0.00007
0.00007
0.00007
0.00006
0.00006
0.00006
0.00006
0.00005
0.00005
0.00005
3.7
0.00011
0.00010
0.00010
0.00010
0.00009
0.00009
0.00008
0.00008
0.00008
0.00008
3.6
0.00016
0.00015
0.00015
0.00014
0.00014
0.00013
0.00013
0.00012
0.00012
0.00011
3.5
0.00023
0.00022
0.00022
0.00021
0.00020
0.00019
0.00019
0.00018
0.00017
0.00017
3.4
0.00034
0.00032
0.00031
0.00030
0.00029
0.00028
0.00027
0.00026
0.00025
0.00024
3.3
0.00048
0.00047
0.00045
0.00043
0.00042
0.00040
0.00039
0.00038
0.00036
0.00035
3.2
0.00069
0.00066
0.00064
0.00062
0.00060
0.00058
0.00056
0.00054
0.00052
0.00050
3.1
0.00097
0.00094
0.00090
0.00087
0.00084
0.00082
0.00079
0.00076
0.00074
0.00071
3.0
0.00135
0.00131
0.00126
0.00122
0.00118
0.00114
0.00111
0.00107
0.00103
0.00100
2.9
0.0019
0.0018
0.0018
0.0017
0.0016
0.0016
0.0015
0.0015
0.0014
0.0014
2.8
0.0026
0.0025
0.0024
0.0023
0.0023
0.0022
0.0021
0.0021
0.0020
0.0019
2.7
0.0035
0.0034
0.0033
0.0032
0.0031
0.0030
0.0029
0.0028
0.0027
0.0026
2.6
0.0047
0.0045
0.0044
0.0043
0.0041
0.0040
0.0039
0.0038
0.0037
0.0036
2.5
0.0062
0.0060
0.0059
0.0057
0.0055
0.0054
0.0052
0.0051
0.0049
0.0048
2.4
0.0082
0.0080
0.0078
0.0075
0.0073
0.0071
0.0069
0.0068
0.0066
0.0064
2.3
0.0107
0.0104
0.0102
0.0099
0.0096
0.0094
0.0091
0.0089
0.0087
0.0084
2.2
0.0139
0.0136
0.0132
0.0129
0.0125
0.0122
0.0119
0.0116
0.0113
0.0110
2.1
0.0179
0.0174
0.0170
0.0166
0.0162
0.0158
0.0154
0.0150
0.0146
0.0143
2.0
0.0228
0.0222
0.0217
0.0212
0.0207
0.0202
0.0197
0.0192
0.0188
0.0183
1.9
0.0287
0.0281
0.0274
0.0268
0.0262
0.0256
0.0250
0.0244
0.0239
0.0233
1.8
0.0359
0.0351
0.0344
0.0336
0.0329
0.0322
0.0314
0.0307
0.0301
0.0294
1.7
0.0446
0.0436
0.0427
0.0418
0.0409
0.0401
0.0392
0.0384
0.0375
0.0367
1.6
0.0548
0.0537
0.0526
0.0516
0.0505
0.0495
0.0485
0.0475
0.0465
0.0455
1.5
0.0668
0.0655
0.0643
0.0630
0.0618
0.0606
0.0594
0.0582
0.0571
0.0559
1.4
0.0808
0.0793
0.0778
0.0764
0.0749
0.0735
0.0721
0.0708
0.0694
0.0681
1.3
0.0968
0.0951
0.0934
0.0918
0.0901
0.0885
0.0869
0.0853
0.0838
0.0823
1.2
0.1151
0.1131
0.1112
0.1093
0.1075
0.1056
0.1038
0.1020
0.1003
0.0985
1.1
0.1357
0.1335
0.1314
0.1292
0.1271
0.1251
0.1230
0.1210
0.1190
0.1170
1.0
0.1587
0.1562
0.1539
0.1515
0.1492
0.1469
0.1446
0.1423
0.1401
0.1379
0.9
0.1841
0.1814
0.1788
0.1762
0.1736
0.1711
0.1685
0.1660
0.1635
0.1611
0.8
0.2119
0.2090
0.2061
0.2033
0.2005
0.1977
0.1949
0.1922
0.1894
0.1867
0.7
0.2420
0.2389
0.2358
0.2327
0.2296
0.2266
0.2236
0.2206
0.2177
0.2148
0.6
0.2743
0.2709
0.2676
0.2643
0.2611
0.2578
0.2546
0.2514
0.2483
0.2451
0.5
0.3085
0.3050
0.3015
0.2981
0.2946
0.2912
0.2877
0.2843
0.2810
0.2776
0.4
0.3446
0.3409
0.3372
0.3336
0.3300
0.3264
0.3228
0.3192
0.3156
0.3121
0.3
0.3821
0.3783
0.3745
0.3707
0.3669
0.3632
0.3594
0.3557
0.3520
0.3483
0.2
0.4207
0.4168
0.4129
0.4090
0.4052
0.4013
0.3974
0.3936
0.3897
0.3859
0.1
0.4602
0.4562
0.4522
0.4483
0.4443
0.4404
0.4364
0.4325
0.4286
0.4247
0.0
0.5000
0.4960
0.4920
0.4880
0.4840
0.4801
0.4761
0.4721
0.4681
0.4641
Cumulative Probabilities
Z
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.0
0.5000
0.5040
0.5080
0.5120
0.5160
0.5199
0.5239
0.5279
0.5319
0.5359
0.1
0.5398
0.5438
0.5478
0.5517
0.5557
0.5596
0.5636
0.5675
0.5714
0.5753
0.2
0.5793
0.5832
0.5871
0.5910
0.5948
0.5987
0.6026
0.6064
0.6103
0.6141
0.3
0.6179
0.6217
0.6255
0.6293
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
0.5
0.6915
0.6950
0.6985
0.7019
0.7054
0.7088
0.7123
0.7157
0.7190
0.7224
0.6
0.7257
0.7291
0.7324
0.7357
0.7389
0.7422
0.7454
0.7486
0.7517
0.7549
0.7
0.7580
0.7611
0.7642
0.7673
0.7704
0.7734
0.7764
0.7794
0.7823
0.7852
0.8
0.7881
0.7910
0.7939
0.7967
0.7995
0.8023
0.8051
0.8078
0.8106
0.8133
0.9
0.8159
0.8186
0.8212
0.8238
0.8264
0.8289
0.8315
0.8340
0.8365
0.8389
1.0
0.8413
0.8438
0.8461
0.8485
0.8508
0.8531
0.8554
0.8577
0.8599
0.8621
1.1
0.8643
0.8665
0.8686
0.8708
0.8729
0.8749
0.8770
0.8790
0.8810
0.8830
1.2
0.8849
0.8869
0.8888
0.8907
0.8925
0.8944
0.8962
0.8980
0.8997
0.9015
1.3
0.9032
0.9049
0.9066
0.9082
0.9099
0.9115
0.9131
0.9147
0.9162
0.9177
1.4
0.9192
0.9207
0.9222
0.9236
0.9251
0.9265
0.9279
0.9292
0.9306
0.9319
1.5
0.9332
0.9345
0.9357
0.9370
0.9382
0.9394
0.9406
0.9418
0.9429
0.9441
1.6
0.9452
0.9463
0.9474
0.9484
0.9495
0.9505
0.9515
0.9525
0.9535
0.9545
1.7
0.9554
0.9564
0.9573
0.9582
0.9591
0.9599
0.9608
0.9616
0.9625
0.9633
1.8
0.9641
0.9649
0.9656
0.9664
0.9671
0.9678
0.9686
0.9693
0.9699
0.9706
1.9
0.9713
0.9719
0.9726
0.9732
0.9738
0.9744
0.9750
0.9756
0.9761
0.9767
2.0
0.9772
0.9778
0.9783
0.9788
0.9793
0.9798
0.9803
0.9808
0.9812
0.9817
2.1
0.9821
0.9826
0.9830
0.9834
0.9838
0.9842
0.9846
0.9850
0.9854
0.9857
2.2
0.9861
0.9864
0.9868
0.9871
0.9875
0.9878
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
2.4
0.9918
0.9920
0.9922
0.9925
0.9927
0.9929
0.9931
0.9932
0.9934
0.9936
2.5
0.9938
0.9940
0.9941
0.9943
0.9945
0.9946
0.9948
0.9949
0.9951
0.9952
2.6
0.9953
0.9955
0.9956
0.9957
0.9959
0.9960
0.9961
0.9962
0.9963
0.9964
2.7
0.9965
0.9966
0.9967
0.9968
0.9969
0.9970
0.9971
0.9972
0.9973
0.9974
2.8
0.9974
0.9975
0.9976
0.9977
0.9977
0.9978
0.9979
0.9979
0.9980
0.9981
2.9
0.9981
0.9982
0.9982
0.9983
0.9984
0.9984
0.9985
0.9985
0.9986
0.9986
3.0
0.99865
0.99869
0.99874
0.99878
0.99882
0.99886
0.99889
0.99893
0.99897
0.99900
3.1
0.99903
0.99906
0.99910
0.99913
0.99916
0.99918
0.99921
0.99924
0.99926
0.99929
3.2
0.99931
0.99934
0.99936
0.99938
0.99940
0.99942
0.99944
0.99946
0.99948
0.99950
3.3
0.99952
0.99953
0.99955
0.99957
0.99958
0.99960
0.99961
0.99962
0.99964
0.99965
3.4
0.99966
0.99968
0.99969
0.99970
0.99971
0.99972
0.99973
0.99974
0.99975
0.99976
3.5
0.99977
0.99978
0.99978
0.99979
0.99980
0.99981
0.99981
0.99982
0.99983
0.99983
3.6
0.99984
0.99985
0.99985
0.99986
0.99986
0.99987
0.99987
0.99988
0.99988
0.99989
3.7
0.99989
0.99990
0.99990
0.99990
0.99991
0.99991
0.99992
0.99992
0.99992
0.99992
3.8
0.99993
0.99993
0.99993
0.99994
0.99994
0.99994
0.99994
0.99995
0.99995
0.99995
3.9
0.99995
0.99995
0.99996
0.99996
0.99996
0.99996
0.99996
0.99996
0.99997
0.99997
4.0
0.999968329
4.5
0.999996602
5.0
0.999999713
5.5
0.999999981
6.0
0.999999999
Step by Step Solution
There are 3 Steps involved in it
Step: 1
Get Instant Access to Expert-Tailored Solutions
See step-by-step solutions with expert insights and AI powered tools for academic success
Step: 2
Step: 3
Ace Your Homework with AI
Get the answers you need in no time with our AI-driven, step-by-step assistance
Get Started
Elementary Number Theory
Authors: Charles Vanden Eynden
2nd Edition
1478639113, 9781478639114
