Find the Z-score such that the area under the standard normal curve to the left is 0.52. Click the icon to view a table of areas under the normal curve. is the Z-score such that the area under the curve to the left is 0.52. (Round to two decimal places as needed.)
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
![i Tables of Areas under the Normal Curve
TABLE V
Standard Normal Distribution
.02
00
.01
.03
.04
.05
.06
.07
.08 09
Area
-34
-33
-3.2
0.0003 0.0003 0.0003
0.0005
0.0007 0.0007 0.0006
0.0003
0.0004
0.0003
0.0004
0.0003 0.0003 0.0003
0.0004
0.0006
0.0003 0.0002
0.0004
0.0003
0.0005
0.0005
0.0005 0.0005
0.0004
0.0006
0.0004
0.0005
0.0006
0.0006
0.0009 0.0008
0.0010
0.0009
-31
-3.0
0.0009
0.0008
0.0008
0.0008
0.0007 0.0007
0.0010
0.0010
0.0013 0.0013 0.0013 0.0012
0.0012 0.001l 0.0011
0.0011
-29
-28
-27
0.0019 0.0018 0.0018
0.0026 0.0025 0.0024
0.0035
0.0017
0.0023
0.0032
0.0016
0.0023
0.0031
0.0016 0.0015
0.0021
0.0029
0.0015
0.0021
0.0028
0.0014
0.0020
0.0027
0.0014
0.0019
0.0026
0.0022
0.0034
0.0033
0.0030
-26
-2.5
0.0047 0.0045
0.0062
0.0044 0.0043 0.0041
0.0055
0.0040 0.0039 0.0038 0.0037 0.0036
0.0054 0.0052 0.0051
0.0060 0.0059 0.0057
0.0049 0.0048
0.0080
0.0068
0.0089
0.0116
0.0150
0.0192
-24
-23
-2.2
0.0066 0.0064
0.0087
0.0082
0.0078 0.0075 0.0073 0.0071
0.0094
0.0122
0.0158
0.0202
0.0069
0.0091
0.0119
0.0154
0.0197
0.0102
0.0099
0.0139 0.0136 0.0132 0.0129
0.0179 0.0174 0.0170 0.0166
0.0212
0.0107
0.0104
0.0096
0.0125
0.0084
0.0113 0.0110
00146 00143
0.0188 0.0183
-21
-20
0.0162
0.0207
0.0228 0.0222
0.0217
-19
-18
-1.7
-16
-1.5
0.0287 0.0281
0.0359 0.0351
0.0446 0.0436
0.0548 0.0537
0.0668 0.0655
0.0268
0.0344 0.03346
0.0427
0.0274
0.0418
0.0526 0.0516
0.0630
0.0262
0.0329
0.0409
0.0505
0.0618
0.0256
0.0322
0.0401
0.0495
0.0250
0.0314
0.0392
0.0485
0.0244
0.0307
0.0384
0.0475
0.0582
0.0239
0.0301
0.0375
0.0465
0.0571
0.0233
0.0294
0.0367
0.0455
0.0559
0.0643
0.0606
0.0594
0.0749
-14
-13
-1.2
-11
0.0808 0.0793 0.0778 0.0764
0.0934
0.1151 0.1131 0.1112 0.1093
0.1314
0.1562 0.1539 0.1515 0.1492
0.0735 0.0721
0.0869
0.1038
0.1230
0.1469 0.1446 0.1423 0.1401
0.0708
0.0853
0.1020
0.1210
0.0694
0.0838
0.1003
0.0681
0.0823
0.0985
0.1190 0.1170
0.1379
0.0968 0.0951
0.0918
0.0901
0.1075
0.1271
0.0885
0.1056
0.1251
0.1357 0.1335
0.1587
0.1292
-10
0.1788 0.1762 0.1736
0.2005
0.2296
0.2611
0.2946
0.1685 0.1660 0.1635 0.1611
-0.9
-08
-0.7
0.1841 0.1814
0.2119 0.2090 0.2061 0.2033
0.2420 0.2389 0.2358 0.2327
0.2743 0.2709 0.2676 0.2643
0.3085 0.3050 0.3015
0.1711
0.1977 0.1949 0.1922
0.2266
0.1894
02177
0.1867
0.2148
0.2206
0.2578 0.2546 0.2514 0.2483 0.2451
0.2236
-06
-0.5
0.2981
0.2912 0.2877 0.2843
0.2810 0.2776
-04
-0.3
-0.2
-0.1
-0.0
0.0
0.1
0.3446 0.3409 0.3372 0.3336
0.3783 03745 0.3707
0.4168 0.4129
0.4562 0.4522 0.4483
0.3300
0.3669
0.4052
0.4443
0.4840
0.5160 0.5199 0.5239
0.5557
0.3264 0.3228 0.3192
0.3632 0.3594 0.3557
0.3936
0.4325
0.4721
0.5279
0.5675
0.3156 0.3121
0.3520
0.3821
0.4207
0.4602
0.3483
0.4013 0.3974
0.4404 0.4364
0.4090
0.3897
0.3859
0.4247
0.4681 0.4641
0.5319
0.4286
0.5000 0.4960 04920
0.5040
0.5438 0.5478
0.4880
0.5080 0.5120
0.5517
0.4801
0.4761
0.5000
0.5398
0.5359
0.714 0.5753
0.5596 0.5636
0.2
0.3
0.4
0.5793
0.6179
0.6554 0.6591
0.5948
0.6331
0.6700
0.6026
0.6368 0.6406
0.6736 0.6772
0.6064
0.6443
0.6808
0.5832
0.5871
0.6217 0.6255
0.6628
0.5910
0.6293
0.6664
0.5987
0.6103
0.6480
0.6844
0.6141
0.6517
0.6879
0.5
0.6
0.6915
0.7257
0.6950 0.698S
0.7291
0.7224
0.7324 0.7357 0.7389 0.7422 0.7454 0.7486 0.7517 0.7549
0.7019 0.7054 0.7088 0.7123
0.7157 0.7190
0.7
0.7580 0.7611
0.7881
0.7910
0.8159
0.7642 0.7673 0.7704 0.7734 0.7764
0.7939 0.7967 0.7995 0.8023 0.8051
0.8264
0.7794 0.7823 0.7852
0.8078 0.8106 0.8133
0,8340
0.9
0.8186 0.8212 0.8238
0.8289
0.8315
0.8365
0.8389
0.8554
0.8749 0.8770
0.8962
LO
0.8413
0.8438 0.8461 0.8485 0.8508 0.8531
0,8665
0.8869
0.8577 0.8599 0.8621
0.8790
0.8980
0.9147 0.9162 0.9177
0.9292
1.1
0.8686
0.8888
0.9066
0.9222 0.9236 0.9251
0.8708
0.8907 0.8925 0.8944
0.8810
0.8997
0.8643
0.8729
0.8830
0.9015
1.2
0.8849
1.3
0.9032
14
0.9192 0.9207
0.9049
0.9082
0.9099
0.9115
0.9131
0.9265 0.9279
0.9306
0.9319
0.9345
0.9463
1.5
16
1.7
1.8
1.9
0.9332
0.9452
0,9554
0.9641
0.9713
0.9484
0.9564 0.9573 0.9582 0.9591 0.9599
0.9649 0.9656 0.9664 0.9671 0.9678 0.9686
0.9719 0.9726 0.9732 0.9738 0.9744
0.9357 0.9370 0.9382 0.9394 0.9406
0.9495
0.9418
0.9525
0.9616
0.9429 0.9441
0.9535
0.9625
0.9693 0.9699 0.9706
0.9761 0.9767
0.9474
0.9505
0.9515
0.9608
0.9545
0.9633
0.9750 0.9756
20
2.1
22
2.3
24
0.9772 0.9778 0.9783 0.9788 0.9793 0.9798
0.9826 0.9830 0.9834
0.9871
0.9812 0.9817
0.9854
0.9857
0.9887 0.9890
0.9821
0.9861
0.9893
0.9803
0.9846
0.9808
0.9850
0.9884
0.9838 0.9842
0.9875 0.9878
0.9864 0.9868
0.9881
0.9896 0.9898 0.9901
0.9920 0.9922 0.9925
0.9904
0.9927
0.9906
0.9929
0.9909
0.9931
0.9911 0.9913
0.9932
0.9934
0.9916
0,9918
0.9936
2.5
26
27
0.9938
0.9943 0.9945 0.9946
0.9956 0.9957 0.9959 0.9960
0.9940 0.9941
0.9955
0.9966 0.9967
0.9975
0.9948
0.9961
0.9969 0.9970 0.9971
0.9949
0.9962
0.9951
0.9963
0.9972 0.9973
0.9980
0.9986
0.9952
0.9964
0.9974
0.9981
0.9986
0,9953
0.9965
0.9968
28
29
0.9974
0.9981
0.9976 0.9977 0.9977 0.9978
0.9982
0.9979 0.9979
0.9985
0.9982
0.9983
0.9984 0.9984 0.9985
3.0
3.1
3.2
33
3.4
0.9987 0.9987
0.9990 0.9991
0.9993 0.9993 0.9994 0.9994 0.9994 0.9994
0,9995
0.9997
0.9987 0.9988 0.9988 0.9989 0.9989
0.9991
0.9989
0.9992 0.9992
0.9990
0.9993
0.995 0.9995 0.9995
0.9990
0.9991
0.9992 0.9992
0.9993
0.9994
0.9995
0.9997 0.9997
0.9995 0.9996 0.9996 0.9996 0.9996
0.9997 0.9997 0.9997
0.9996 0.9996 0.9997
0.9997 0.9997
0.9997
0.9998
00
.01
.02
03
.04
.05
.06
.07
.08
.09
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![Find the Z-score such that the area under the standard normal curve to the left is 0.52.
Click the icon to view a table of areas under the normal curve.
is the Z-score such that the area under the curve to the left is 0.52.
(Round to two decimal places as needed.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fda846be0-6ec0-4729-8a28-7bc009bff4bb%2F34529525-a72d-4840-8ac5-d05388670d6f%2F979aae_processed.jpeg&w=3840&q=75)
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