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)).
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)).
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
do part d) and e)
Transcribed Image Text: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.
is the value of K?
What
(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)).
Transcribed Image Text: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.
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