First, we need to calculate a Z-score. The formula is denoted below: Using the Normal Distribution, Calculate P(X < 240)
Z =
X - μ
σ/√1
Z =
240 - 250
7.14/√1
Z =
-10
7.14/1
Z =
-10
7.14
Z = -1.401
From the table below, we see that our Z value is = 0.419243
The z-table probability runs from 0 to z and -z to 0, so we lookup our value From the table below, we find our value of 0.419243 Since that represents ½ of the graph, we subtract our value from 0.5 → 0.5 - 0.419243 P(x<-1.401) = 0.080757
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0
0
0.004
0.008
0.012
0.016
0.0199
0.0239
0.0279
0.0319
0.0359
0.1
0.0398
0.0438
0.0478
0.0517
0.0557
0.0596
0.0636
0.0675
0.0714
0.0753
0.2
0.0793
0.0832
0.0871
0.091
0.0948
0.0987
0.1026
0.1064
0.1103
0.1141
0.3
0.1179
0.1217
0.1255
0.1293
0.1331
0.1368
0.1406
0.1443
0.148
0.1517
0.4
0.1554
0.1591
0.1628
0.1664
0.17
0.1736
0.1772
0.1808
0.1844
0.1879
0.5
0.1915
0.195
0.1985
0.2019
0.2054
0.2088
0.2123
0.2157
0.219
0.2224
0.6
0.2257
0.2291
0.2324
0.2357
0.2389
0.2422
0.2454
0.2486
0.2517
0.2549
0.7
0.258
0.2611
0.2642
0.2673
0.2704
0.2734
0.2764
0.2794
0.2823
0.2852
0.8
0.2881
0.291
0.2939
0.2967
0.2995
0.3023
0.3051
0.3078
0.3106
0.3133
0.9
0.3159
0.3186
0.3212
0.3238
0.3264
0.3289
0.3315
0.334
0.3365
0.3389
1
0.3413
0.3438
0.3461
0.3485
0.3508
0.3531
0.3554
0.3577
0.3599
0.3621
1.1
0.3643
0.3665
0.3686
0.3708
0.3729
0.3749
0.377
0.379
0.381
0.383
1.2
0.3849
0.3869
0.3888
0.3907
0.3925
0.3944
0.3962
0.398
0.3997
0.4015
1.3
0.4032
0.4049
0.4066
0.4082
0.4099
0.4115
0.4131
0.4147
0.4162
0.4177
1.4
0.4192
0.4207
0.4222
0.4236
0.4251
0.4265
0.4279
0.4292
0.4306
0.4319
1.5
0.4332
0.4345
0.4357
0.437
0.4382
0.4394
0.4406
0.4418
0.4429
0.4441
1.6
0.4452
0.4463
0.4474
0.4484
0.4495
0.4505
0.4515
0.4525
0.4535
0.4545
1.7
0.4554
0.4564
0.4573
0.4582
0.4591
0.4599
0.4608
0.4616
0.4625
0.4633
1.8
0.4641
0.4649
0.4656
0.4664
0.4671
0.4678
0.4686
0.4693
0.4699
0.4706
1.9
0.4713
0.4719
0.4726
0.4732
0.4738
0.4744
0.475
0.4756
0.4761
0.4767
2
0.4772
0.4778
0.4783
0.4788
0.4793
0.4798
0.4803
0.4808
0.4812
0.4817
2.1
0.4821
0.4826
0.483
0.4834
0.4838
0.4842
0.4846
0.485
0.4854
0.4857
2.2
0.4861
0.4864
0.4868
0.4871
0.4875
0.4878
0.4881
0.4884
0.4887
0.489
2.3
0.4893
0.4896
0.4898
0.4901
0.4904
0.4906
0.4909
0.4911
0.4913
0.4916
2.4
0.4918
0.492
0.4922
0.4925
0.4927
0.4929
0.4931
0.4932
0.4934
0.4936
2.5
0.4938
0.494
0.4941
0.4943
0.4945
0.4946
0.4948
0.4949
0.4951
0.4952
2.6
0.4953
0.4955
0.4956
0.4957
0.4959
0.496
0.4961
0.4962
0.4963
0.4964
2.7
0.4965
0.4966
0.4967
0.4968
0.4969
0.497
0.4971
0.4972
0.4973
0.4974
2.8
0.4974
0.4975
0.4976
0.4977
0.4977
0.4978
0.4979
0.4979
0.498
0.4981
2.9
0.4981
0.4982
0.4982
0.4983
0.4984
0.4984
0.4985
0.4985
0.4986
0.4986
3
0.4987
0.4987
0.4987
0.4988
0.4988
0.4989
0.4989
0.4989
0.499
0.499
NOTE: To get in Microsoft Excel using your z-score, enter the formula =NORMSDIST(-1.401)
P(x<-1.401) = 0.080757
What is the Answer?
P(x<-1.401) = 0.080757
How does the Normal Distribution Calculator work?
Free Normal Distribution Calculator - Calculates the probability that a random variable is less than or greater than a value or between 2 values using the Normal Distribution z-score (z value) method (Central Limit Theorem).
Also calculates the Range of values for the 68-95-99.7 rule, or three-sigma rule, or empirical rule. Calculates z score probability This calculator has 4 inputs.
What 1 formula is used for the Normal Distribution Calculator?
What 9 concepts are covered in the Normal Distribution Calculator?
distribution
value range for a variable
empirical rule
Provides estimate for the spread of data in a normal distribution. 68% of the data will fall within one standard deviation of the mean. 95% of the data will fall within two standard deviations of the mean. 99.7% of the data will fall within three standard deviations of the mean
event
a set of outcomes of an experiment to which a probability is assigned.
mean
A statistical measurement also known as the average
normal distribution
an arrangement of a data set in which most values cluster in the middle of the range and the rest taper off symmetrically toward either extreme.
probability
the likelihood of an event happening. This value is always between 0 and 1. P(Event Happening) = Number of Ways the Even Can Happen / Total Number of Outcomes
standard deviation
a measure of the amount of variation or dispersion of a set of values. The square root of variance
variance
How far a set of random numbers are spead out from the mean
z score
the number of standard deviations from the mean a data point is. Also known as a standard score
Example calculations for the Normal Distribution Calculator
