If
X=115,
σ=22,
and
n=36,
construct a
95%
confidence
interval estimate of the population mean, μ.
Click here to view page 1 of the cumulative standardised
normal distribution table.
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Click here to view page 2 of the cumulative standardised normal distribution table.
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The
95%
confidence interval is
enter your response here≤μ≤enter your response here.
(Round to two decimal places as needed.)
Transcribed Image Text: Entry represents area under the cumulative standardised normal distribution from - co to Z.
Cumulative Probabilities
0.01
0.03
0.04
0.05
0.06
0.08
0.09
0.00
0.02
0.07
--6.0
0.000000001
-5.5
-5.0
0.000000019
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
0.00004
0.00003
0.00003
0.00007
0.00005
--3.8
-3.7
0.00007
0.00011
0.00007
0.00006
0.00010
0.00006
0.00006
0.00006
0.00005
0.00008
0.00005
0.00008
0.00010
0.00010
0.00009
0.00009
0.00008
0.00008
-3.6
-3.5
0.00016
0.00015
0.00015
0.00014
0.00014
0.00013
0.00013
0.00012
0.00012
0.00011
0.00023
0.00022
0.00022
0.00021
0.00020
0.00019
0.00019
0.00018
0.00017
0.00017
0.00024
0.00025
0.00036
0.00052
-3.4
0.00034
0.00032
0.00031
0.00030
0.00029
0.00028
0.00027
0.00026
0.00035
0.00050
0.00071
-3.3
0.00048
0.00047
0.00045
0.00043
0.00042
0.00040
0.00039
0.00038
-3.2
0.00069
0.00066
0.00064
0.00062
0.00058
0.00056
0.00054
0.00060
0.00084
-3.1
0.00097
0.00094
0.00090
0.00087
0.00082
0.00079
0.00076
0.00074
-3.0
0.00135
0.00131
0.00126
0.00118
0.0016
0.00114
0.00111
0.00103
0.00122
0.0017
0.00107
0.00100
-2.9
0.0019
0.0018
0.0018
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
0.0059
0.0078
-2.5
0.0062
0.0060
0.0052
0.0051
0.0049
0.0048
0.0057
0.0075
0.0055
0.0054
0.0071
-2.4
0.0082
0.0080
0.0073
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
0.0136
0.0132
0.0125
0.0122
0.0139
0.0179
0.0129
0.0166
0.0119
0.0116
0.0113
0.0110
0.0143
-2.1
0.0174
0.0170
0.0162
0.0158
0.0154
0.0150
0.0146
-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
0.0359
0.0281
0.0274
0.0268
0.0262
0.0256
0.0250
0.0244
0.0239
0.0233
-1.8
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
0.0548
0.0537
0.0526
0.0516
0.0505
0.0485
0.0475
0.0455
0.0559
-1.6
0.0495
0.0606
0.0465
0.0571
-1.5
0.0668
0.0655
0.0643
0.0630
0.0618
0.0594
0.0582
-1.4
0.0808
0.0793
0.0778
0.0764
0.0749
0.0735
0.0721
0.0708
0.0694
0.0681
0.0853
0.0838
0.1003
-1.3
0.0968
0.0951
0.0934
0.0918
0.0901
0.0885
0.0869
0.0823
-1.2
0.1151
0.1131
0.1112
0.1093
0.1075
0.1056
0.1038
0.1020
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
0.1379
0.1492
0.1736
0.1469
0.1446
0.1423
0.1401
-0.9
0.1841
0.1814
0.1788
0.1762
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
0.2388
0.2358
0.2327
0.2296
0.2266
0.2236
0.2206
0.2177
0.2148
0.2451
-0.6
0.2743
0.2709
0.2676
0.2643
0.2611
0.2578
0.2546
0.25 14
0.2482
-0.5
0.3085
0.3050
0.3015
0.2981
0.2946
0.2912
0.2877
0.2843
0.28 10
0.2776
-0.4
0.3446
0.3409
0.3372
0.3336
0.3300
0.3264
0.3228
0.3192
0.3156
0.3121
-03
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
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
Transcribed Image Text: Entry represents area under the cumulative standardised normal distribution from - 0o to Z.
Cumulative Probabilities
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.0
0.5000
0.5080
0.5199
0.5279
0.5040
0.5438
0.5120
0.5517
0.5160
0.5239
0.5319
0.5714
0.5359
0.5753
0.5557
0.5948
0.1
0.5398
0.5478
0.5596
0.5636
0.5675
0.2
0.5793
0.5832
0.5871
0.5910
0.5987
0.6026
0.6064
0.6103
0.6141
0.6217
0.6591
0.6950
0.3
0.6179
0.6255
0.6293
0.6331
0.6368
0.6406
0.6443
0.6808
0.6480
0.6517
0.6554
0.6915
0.4
0.6628
0.6664
0.6700
0.6736
0.6772
0.6844
0.6879
0.5
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
0.7486
0.7422
0.7734
0.7454
0.7518
0.7549
0.7704
0.7995
0.7
0.7580
0.7612
0.7642
0.7673
0.7764
0.7794
0.7823
0.7852
0.8
0.7881
0.7910
0.7939
0.7967
0.8023
0.8051
0.8078
0.8106
0.8133
0.8186
0.8438
0.8238
0.8289
0.8315
0.8554
0.8340
0.8577
0.9
0.8389
0.8159
0.8413
0.8212
0.8264
0.8365
0.8599
1.0
0.8461
0.8485
0.8508
0.8531
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
0.95 15
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
0.9649
0.9656
0.9664
0.9732
0.9671
0.9678
0.9686
0.9750
0.9706
0.9767
1.8
0.9641
0.9693
0.9756
0.9699
1.9
0.9713
0.9719
0.9726
0.9738
0.9744
0.9761
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
0.9868
0.9834
0.9871
0.9838
0.9842
0.9846
0.9881
0.9850
0.9854
0.9857
2.2
0.9861
0.9864
0.9875
0.9878
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
0.9922
0.9941
2.4
0.9918
0.9920
0.9925
0.9927
0.9929
0.9931
0.9932
0.9934
0.9936
2.5
0.9938
0.9940
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
0.99940
0.99958
3.2
0.99931
0.99934
0.99936
0.99938
0.99942
0.99944
0.99946
0.99948
0.99950
3.3
0.99952
0.99953
0.99955
0.99957
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
0.999999713
5.0
5.5
0.999999981
6.0
0.999999999
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.
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