Find the percent of the total area under the standard normal curve between the following z-scores. z=−2.89 and z= 2.03 The percent of the total area between z=−2.89 and z=2.03 is _______%. (Round to the nearest hundredth 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!

 alt="Area Under a Normal Curve to the Left of z, where z =
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0.01
0.02
0.03
0.05
0.06
0.08
0.09
-3.4
-33
-3.2
-3.1
-3.0
0.0003
0.0005
0.0007
0.0010
0.0013
0,0003
0.0003
0.0005
0.000
0.0009
0.0003
0.0004
0.0006
0.0009
0.0012
0.0003
0.0004
0.0006
0.0008
0.0012
0.0003
0.0007
0.0009
0.0013
0.0006
0.0008
0.0011
0.0003
0.0004
0.0006
0.0008
0.0011
0.0003
0.0004
0.0005
0.0008
0.0011
0.0004
0.0005
0.0007
0.0010
0.0002
0.0003
0.0005
0.0007
0.0010
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-2.9
-28
0.0019
0.0026
0.0035
0.0047
81000
0.0017
0.0017
0.0023
0.0032
0.0016
0.0023
0.0016
0.0022
0.0030
0.0040
0.0054
0.0015
0.0021
0.0028
0.0038
0.0051
0.0015
0.0021
0.0014
0.0020
0.0027
0.0037
0.0049
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0.0026
0.0036
0.0048
0.0025
-27
-2.6
-25
0.0034
0.0033
0.0029
0.0039
0.0052
0.0031
0.0045
0.0044
0.0059
0.0043
0.0041
0.0055
0.0062
0.0060
0.0057
-2.4
-2.3
0.0080
0.0104
00136
0.0066
0.0087
00113
00146
00188
0.0064
0.0084
0.0110
0.0143
0.0183
0.0068
0.0089
0.0082
0.0075
0.0099
0.0071
0.0094
0.0122
0.0158
0.0202
0.0073
0.0096
0.0069
0.0091
0.01 19
0.0154
0.0197
0.0078
0.0107
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0.0139
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0.०129
0.0166
0.0212
0.0132
0.0170
0.0217
0.0150
00192
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0,0174
0.0162
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0.0228
0.0222
0.0207
0.0250
0.0314
0.0392
0.0485
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0.0239
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0.0375
0.0465
0.0571
0.0233
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0.0367
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0.0322
0.0401
0.0495
0.0606
0.0262
0.0274
0.0344
0.0427
0.0526
0.0643
0.0268
0.0336
0.0418
0.0516
0.0281
0.0287
0.0359
0.0446
0.0548
-1.9
-1.8
0.0352
0.0329
0.0384
0.0475
0.0582
0.0409
0.0436
0.0537
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-1.6
1.5
0.0505
0,0618
-1.5
0.0668
0.0655
0.0630
0.0722
0,0869
0.1038
0.1230
0,1446
0.0708
0.0853
0.1020
0,1210
0.1423
0,0694
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0.1003
0.1190
0.1401
0.0681
0.0823
0.0985
0.1170
0.1379
0.0735
0.0764
0.0918
0.1093
0.1292
0.1515
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0.0901
0.1075
0.1271
0.1492
0.0793
0.0778
0.0808
0.0968
0.1151
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1.4
0.0885
0.1056
0.1251
0.0951
0,0934
1.3
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0.1112
0.1357
0.1587
0.1131
0.1335
0.1562
0.1314
0.1539
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0.1894
02177
0.2483
0.2810
0.1611
0 1867
0.2148
0.2451
02776
0,1660
0,1922
0,1685
0,1949
0.2236
0.2546
0.2877
0.1711
0.1814
0.2090
0.2389
0.2709
0.3050
0.1788
0.2061
0,2358
0.2676
0.3015
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0.2327
0.2643
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0.2578
0.2912
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0.3897
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0.3192
0.3557
0.3264
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0.3336
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0.490
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