just do part e) and show clearly stepA factory produces cylindrical metal bar. The production process can be modeled by normal distributionwith mean length of 11 cm and standard deviation of 0.25 cm.(a) What is the probability that a randomly selected cylindrical metal bar has a length longer than 10.5 cm?(b) There is 14% chance that a randomly selected cylindrical metal bar has a length longer than K. Whatis the value of K?(c) The production cost of a metal bar is $80 per cm plus a basic cost of $100. Find the mean, median,standard deviation, variance, and 86th percentile of the production cost of a metal bar.(d) Write a short paragraph (about 30 – 50 words) to summarize the production cost of a metal bar. (Thesummary needs to include all summary statistics found in part (c)).(e) In order to minimize the chance of the production cost of a metal bar to be more expensive than $1000,the senior manager decides to adjust the production process of the metal bar. The mean length is fixedand can’t be changed while the standard deviation can be adjusted. Should the process standarddeviation be adjusted to (I) a higher level than 0.25 cm, or (II) a lower level than 0.25 cm? (Write downyour suggestion, no explanation is needed in part (e)). The entries in Table I are the probabilities that a random variable having thestandard normal distribution will take on a value between 0 andz. They are givenby the area of the gray region under the curve in the figure.TABLE INORMAL-CURVE AREAS0.000.010.020.030.040.050.060.070.080.090.00000.03980.07930.11790.15540.03590.07530.11410.15170.18790.01200.05170.00.00400.00800.01600.01990.02390.02790.03190.10.04380.04780.05570.05960.06360.06750.07140.10640.14430.18080.20.08320.08710.09100.09480.09870.10260.11030.12170.15910.12550.16280.19850.12930.16640.13680.17360.14060.17720.14800.18440.30.13310.40.17000.50.19150.19500.20190.20540.20880.21230.21570.21900.22240.25490.28520.60.22570.22910.23240.23570.23890.24220.24540.24860.25170.70.25800.26110.26420.26730.27040.27340.27640.27940.28230.80.28810.29100.29390.29670.29950.30230.30510.30780.31060.31330.90.31590.31860.32120.32380.32640.32890.33150.33400.33650.33891.00.34130.34380.34610.34850.35080.35310.35540.35770.35990.36211.10.36430.36650.36860.37080.37290.37490.37700.37900.38100.38301.20.38490.38690.38880.39070.39250.39440.39620.39800.39970.40150.40490.40820.42360.43700.41150.42650.43941.30.40320.40660.40990.41310.41470.41620.41770.41920.43320.42070.43450.42510.43820.42790.44061.40.42220.42920.43060.43191.50.43570.44180.44290.44411.60.44520.44630.44740.44840.44950.45050.45150.45250.45350.45451.70.45540.45640.45730.45820.45910.45990.46080.46160.46250.46331.80.46410.46480.46560.46640.46710.46780.46850.46920.46990.47061.90.47130.47190.47250.47320.47380.47440.47500.47560.47610.47672.00.47720.47780.47830.47880.47930.47980.48030.48080.48120.48170.48340.48710.49010.48380.48750.49040.48460.48810.49090.49310.48570.48900.49160.49360.49522.10.48210.48260.48300.48420.48500.48540.48610.48930.48640.48960.48840.49110.48870.49132.20.48680.48780.48980.49220.49412.30.49062.40.49180.49200.49250.49270.49290.49320.49342.50.49380.49400.49430.49450.49460.49480.49490.49510.49590.49690.49772.60.49530.49550.49560.49570.49600.49610.49620.49630.49642.70.49650.49660.49670.49680.49700.49710.49720.49730.49742.80.49740.49750.49760.49770.49780.49790.49790.49800.49810.49850.49892.90.49810.49820.49820.49830.49840.49840.49850.49860.49863.00.49870.49870.49870.49880.49880.49890.49890.49900.4990Also, for z= 4.0, 5.0 and 6.0, the areas are 0.49997, 0.4999997, and 0.499999999.

Answered: A factory produces cylindrical metal…

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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Related questions

Question

just do part e) and show clearly step

A factory produces cylindrical metal bar. The production process can be modeled by normal distribution
with mean length of 11 cm and standard deviation of 0.25 cm.
(a) What is the probability that a randomly selected cylindrical metal bar has a length longer than 10.5 cm?
(b) There is 14% chance that a randomly selected cylindrical metal bar has a length longer than K. What
is the value of K?
(c) The production cost of a metal bar is $80 per cm plus a basic cost of $100. Find the mean, median,
standard deviation, variance, and 86th percentile of the production cost of a metal bar.
(d) Write a short paragraph (about 30 – 50 words) to summarize the production cost of a metal bar. (The
summary needs to include all summary statistics found in part (c)).
(e) In order to minimize the chance of the production cost of a metal bar to be more expensive than $1000,
the senior manager decides to adjust the production process of the metal bar. The mean length is fixed
and can’t be changed while the standard deviation can be adjusted. Should the process standard
deviation be adjusted to (I) a higher level than 0.25 cm, or (II) a lower level than 0.25 cm? (Write down
your suggestion, no explanation is needed in part (e)).

The entries in Table I are the probabilities that a random variable having the
standard normal distribution will take on a value between 0 andz. They are given
by the area of the gray region under the curve in the figure.
TABLE I
NORMAL-CURVE AREAS
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.0000
0.0398
0.0793
0.1179
0.1554
0.0359
0.0753
0.1141
0.1517
0.1879
0.0120
0.0517
0.0
0.0040
0.0080
0.0160
0.0199
0.0239
0.0279
0.0319
0.1
0.0438
0.0478
0.0557
0.0596
0.0636
0.0675
0.0714
0.1064
0.1443
0.1808
0.2
0.0832
0.0871
0.0910
0.0948
0.0987
0.1026
0.1103
0.1217
0.1591
0.1255
0.1628
0.1985
0.1293
0.1664
0.1368
0.1736
0.1406
0.1772
0.1480
0.1844
0.3
0.1331
0.4
0.1700
0.5
0.1915
0.1950
0.2019
0.2054
0.2088
0.2123
0.2157
0.2190
0.2224
0.2549
0.2852
0.6
0.2257
0.2291
0.2324
0.2357
0.2389
0.2422
0.2454
0.2486
0.2517
0.7
0.2580
0.2611
0.2642
0.2673
0.2704
0.2734
0.2764
0.2794
0.2823
0.8
0.2881
0.2910
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
0.3340
0.3365
0.3389
1.0
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
0.3770
0.3790
0.3810
0.3830
1.2
0.3849
0.3869
0.3888
0.3907
0.3925
0.3944
0.3962
0.3980
0.3997
0.4015
0.4049
0.4082
0.4236
0.4370
0.4115
0.4265
0.4394
1.3
0.4032
0.4066
0.4099
0.4131
0.4147
0.4162
0.4177
0.4192
0.4332
0.4207
0.4345
0.4251
0.4382
0.4279
0.4406
1.4
0.4222
0.4292
0.4306
0.4319
1.5
0.4357
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
0.4648
0.4656
0.4664
0.4671
0.4678
0.4685
0.4692
0.4699
0.4706
1.9
0.4713
0.4719
0.4725
0.4732
0.4738
0.4744
0.4750
0.4756
0.4761
0.4767
2.0
0.4772
0.4778
0.4783
0.4788
0.4793
0.4798
0.4803
0.4808
0.4812
0.4817
0.4834
0.4871
0.4901
0.4838
0.4875
0.4904
0.4846
0.4881
0.4909
0.4931
0.4857
0.4890
0.4916
0.4936
0.4952
2.1
0.4821
0.4826
0.4830
0.4842
0.4850
0.4854
0.4861
0.4893
0.4864
0.4896
0.4884
0.4911
0.4887
0.4913
2.2
0.4868
0.4878
0.4898
0.4922
0.4941
2.3
0.4906
2.4
0.4918
0.4920
0.4925
0.4927
0.4929
0.4932
0.4934
2.5
0.4938
0.4940
0.4943
0.4945
0.4946
0.4948
0.4949
0.4951
0.4959
0.4969
0.4977
2.6
0.4953
0.4955
0.4956
0.4957
0.4960
0.4961
0.4962
0.4963
0.4964
2.7
0.4965
0.4966
0.4967
0.4968
0.4970
0.4971
0.4972
0.4973
0.4974
2.8
0.4974
0.4975
0.4976
0.4977
0.4978
0.4979
0.4979
0.4980
0.4981
0.4985
0.4989
2.9
0.4981
0.4982
0.4982
0.4983
0.4984
0.4984
0.4985
0.4986
0.4986
3.0
0.4987
0.4987
0.4987
0.4988
0.4988
0.4989
0.4989
0.4990
0.4990
Also, for z= 4.0, 5.0 and 6.0, the areas are 0.49997, 0.4999997, and 0.499999999.

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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