A 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)).please do part d and part e thank you 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.

As per the Bartleby guildlines we have to solve first three subparts and rest can be reposted....…

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

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)).

please do part d and part e thank you

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.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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