A batch of 3000 inverters from the production line has a mean output voltage of 337.8 V and the Standard deviation of the output voltage is 3.105. If the voltages of the produced inverters are assumed to be normally distributed, determine the following:The number of inverters with output voltages greater than 336.9 V.The number of inverters with output voltages less than 337.1 V,The number of inverters with output voltages between 336.2 V and 339.8 V. For this problem you should use the table of z-values shown in Figure below. I-01 2 3 4 s6 7 80.00.10.0000 0.0040 0.0080 0.0120 0.0159 0.0199 0.0239 0.0279 0.0319 0.03590.0398 0.0438 0.0478 0.0517 0.0557 0.0596 0.0636 0.0678 0.0714 0.07530.20.30.0793 0.0832 0.0871 0.09100.1179 0.1217 0.1255 0.1293 0.13310.1554 0.1591 0.1628 0.1664 0.1700 0.1736 0.1772 0.18080.1915 0.1950 0.1985 0.2019 0.2054 0.2086 0.2123 0.2157 0.2190 0.22240.0948 0.0987 0.1026 0.1064 0.1103 0.11410.1388 0.1406 0.1443 0.1480 0.15170.1844 0.18790.40.50.60.2257 0.22910.2324 0.2357 0.2389 0.2422 0.2454 0.2486 0.2517 0.25490.70.2580 0.2611 0.2642 0.2673 0.2704 0.2734 0.2760 0.2794 0.2823 0.28520.28810.31590.2910 0.2939 0.29670.3186 0.3212 0.3238 0.32640.34380.29950.3023 0.30510.3289 0.331I5 0.33400.30780.3106 0.31330.33650.80.90.33891.00.34850.3708 0.3729 0.3749 0.3770 0.3790 0.38100.3907 0.3925 0.39440.35310.34130.3643 0.36650.38490.34510.36860.35080.3554 0.3577 0.3599 0.36211.10.38301.20.38690.38880.39620.39800.39970.40151.314150.4032 0.4049 0.4066 0.4082 0.4099 0.41150.41920.4332 0.4345 0,4357 0.4370 0,4382 0.43940.4131 0,4147 0,4162 041770.42920.43060.4207 0.4222 0.4236 042510.42650.42790.43190.4406 0.4418 0.4430 044411.61.70.44520.4554 0.4564 0.4573 0.4582 0.45910.4641 0.4649 0,4656 0,4664 0.46710.47130.4474 0.44840.4495 0.4505 0.45150.45994525 0.45350.46250.46990.45450.46080.46160.46330.47061.80.46780.46860.46931.90.4719 0.4726 0.4732 0.4738 0.4744 0.4750 0.4756 0.4762 047670.4812 0.48170.48080.4850 0.48540.4884 0.48872.00.4772 0.4778 0.47830.4785 0.4793 0.47980.48032.12.20.48210.48610.48930.48260.4830 0,48340.48380.48420.48460.48570.48640.4868 0.48710.48750.48780.48810.48902.30.48960.4898 0.49010.49040.49060.49090.49110.49130.49162.42.50.49200.49220.4940 0.49410.49250.4943 0.4945 0.49460.49180.49270.49290.4932 0,49340.4948 0.4949 0.4951 0.49520.49310.49360.49380.49530.49550.49620.4970 0.4971 0.4972 0.49730.49792.60.4956 0.49570.49590.49600.49610.49630.49642.70.49650.49660.49670.49680.49690.49740.49750.49802.82.90.49740.49810.49780.4982 0.4982 0.4983 0.4984 0.4984 0.4985 0.4985 0.4986 0.49860.49760.49770.49770.49800.49813.00.49870.4987 0.4987 0.4988 0.4988 0.4989 0.4989 0.4989 0.4990 0.49903.10.49900.49910.49910.49910.4992 0.4992 0.4992 0.4992 0.49930.49933.23.30.49930.49930.49940.4995 0.4995 0.49960.49940,49940.49940.49940.49950.4996 0.4996 0.49970.49950.49950.49950.4996 0.4996 0.49963.40.49970.4997 0.4997 0.4997 0.4997 0.4997 0.49970.4997 0.49970.49983.53.63.70.49980.49980.4998 0.4998 0.4998 0.4998 0.49980.49980.4998 0.49980.49980.4998 0.4999 0.4999 0.4999 0.4999 0.4999 0.4999 0.49990.49990.49990.4999 0.4999 0.4999 0.49990.49990.49990.49990.49990.49993.80.49990.4999 0.4999 0.4999 0,4999 0.49990.49990.49990.49990,49993.90.5000 0.5000 0.5000 0.5000 0.5000 0.50000.50000.50000.50000.5000Figure 1: Table of z values for normally distributed curve.

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Answered: A batch of 3000 inverters from the…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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A batch of 3000 inverters from the production line has a mean output voltage of 337.8 V and the Standard deviation of the output voltage is 3.105. If the voltages of the produced inverters are assumed to be normally distributed, determine the following:

The number of inverters with output voltages greater than 336.9 V.
The number of inverters with output voltages less than 337.1 V,
The number of inverters with output voltages between 336.2 V and 339.8 V.

For this problem you should use the table of z-values shown in Figure below.

I-
01 2 3 4 s
6 7 8
0.0
0.1
0.0000 0.0040 0.0080 0.0120 0.0159 0.0199 0.0239 0.0279 0.0319 0.0359
0.0398 0.0438 0.0478 0.0517 0.0557 0.0596 0.0636 0.0678 0.0714 0.0753
0.2
0.3
0.0793 0.0832 0.0871 0.0910
0.1179 0.1217 0.1255 0.1293 0.1331
0.1554 0.1591 0.1628 0.1664 0.1700 0.1736 0.1772 0.1808
0.1915 0.1950 0.1985 0.2019 0.2054 0.2086 0.2123 0.2157 0.2190 0.2224
0.0948 0.0987 0.1026 0.1064 0.1103 0.1141
0.1388 0.1406 0.1443 0.1480 0.1517
0.1844 0.1879
0.4
0.5
0.6
0.2257 0.2291
0.2324 0.2357 0.2389 0.2422 0.2454 0.2486 0.2517 0.2549
0.7
0.2580 0.2611 0.2642 0.2673 0.2704 0.2734 0.2760 0.2794 0.2823 0.2852
0.2881
0.3159
0.2910 0.2939 0.2967
0.3186 0.3212 0.3238 0.3264
0.3438
0.2995
0.3023 0.3051
0.3289 0.331I5 0.3340
0.3078
0.3106 0.3133
0.3365
0.8
0.9
0.3389
1.0
0.3485
0.3708 0.3729 0.3749 0.3770 0.3790 0.3810
0.3907 0.3925 0.3944
0.3531
0.3413
0.3643 0.3665
0.3849
0.3451
0.3686
0.3508
0.3554 0.3577 0.3599 0.3621
1.1
0.3830
1.2
0.3869
0.3888
0.3962
0.3980
0.3997
0.4015
1.3
14
15
0.4032 0.4049 0.4066 0.4082 0.4099 0.4115
0.4192
0.4332 0.4345 0,4357 0.4370 0,4382 0.4394
0.4131 0,4147 0,4162 04177
0.4292
0.4306
0.4207 0.4222 0.4236 04251
0.4265
0.4279
0.4319
0.4406 0.4418 0.4430 04441
1.6
1.7
0.4452
0.4554 0.4564 0.4573 0.4582 0.4591
0.4641 0.4649 0,4656 0,4664 0.4671
0.4713
0.4474 0.4484
0.4495 0.4505 0.4515
0.4599
4525 0.4535
0.4625
0.4699
0.4545
0.4608
0.4616
0.4633
0.4706
1.8
0.4678
0.4686
0.4693
1.9
0.4719 0.4726 0.4732 0.4738 0.4744 0.4750 0.4756 0.4762 04767
0.4812 0.4817
0.4808
0.4850 0.4854
0.4884 0.4887
2.0
0.4772 0.4778 0.4783
0.4785 0.4793 0.4798
0.4803
2.1
2.2
0.4821
0.4861
0.4893
0.4826
0.4830 0,4834
0.4838
0.4842
0.4846
0.4857
0.4864
0.4868 0.4871
0.4875
0.4878
0.4881
0.4890
2.3
0.4896
0.4898 0.4901
0.4904
0.4906
0.4909
0.4911
0.4913
0.4916
2.4
2.5
0.4920
0.4922
0.4940 0.4941
0.4925
0.4943 0.4945 0.4946
0.4918
0.4927
0.4929
0.4932 0,4934
0.4948 0.4949 0.4951 0.4952
0.4931
0.4936
0.4938
0.4953
0.4955
0.4962
0.4970 0.4971 0.4972 0.4973
0.4979
2.6
0.4956 0.4957
0.4959
0.4960
0.4961
0.4963
0.4964
2.7
0.4965
0.4966
0.4967
0.4968
0.4969
0.4974
0.4975
0.4980
2.8
2.9
0.4974
0.4981
0.4978
0.4982 0.4982 0.4983 0.4984 0.4984 0.4985 0.4985 0.4986 0.4986
0.4976
0.4977
0.4977
0.4980
0.4981
3.0
0.4987
0.4987 0.4987 0.4988 0.4988 0.4989 0.4989 0.4989 0.4990 0.4990
3.1
0.4990
0.4991
0.4991
0.4991
0.4992 0.4992 0.4992 0.4992 0.4993
0.4993
3.2
3.3
0.4993
0.4993
0.4994
0.4995 0.4995 0.4996
0.4994
0,4994
0.4994
0.4994
0.4995
0.4996 0.4996 0.4997
0.4995
0.4995
0.4995
0.4996 0.4996 0.4996
3.4
0.4997
0.4997 0.4997 0.4997 0.4997 0.4997 0.4997
0.4997 0.4997
0.4998
3.5
3.6
3.7
0.4998
0.4998
0.4998 0.4998 0.4998 0.4998 0.4998
0.4998
0.4998 0.4998
0.4998
0.4998 0.4999 0.4999 0.4999 0.4999 0.4999 0.4999 0.4999
0.4999
0.4999
0.4999 0.4999 0.4999 0.4999
0.4999
0.4999
0.4999
0.4999
0.4999
3.8
0.4999
0.4999 0.4999 0.4999 0,4999 0.4999
0.4999
0.4999
0.4999
0,4999
3.9
0.5000 0.5000 0.5000 0.5000 0.5000 0.5000
0.5000
0.5000
0.5000
0.5000
Figure 1: Table of z values for normally distributed curve.

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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