A factory produces cylindrical metal bar. The production process can be modeled by normal distribution with mean length

[answerhappygod]

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.
(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
0.01 0.02
0.0040 0.0080 0.0438 0.0478 0.0832 0.0871 0.1217 0.1255 0.1591
0.1628 0.1950 0.1985
0.2291 0.2324 0.2611 0.2642 0.2910 0.2939 0.3186 0.3212 0.3438
0.3461
0.3665 0.3686 0.3869 0.3888 0.4049 0.4066 0.4207 0.4222 0.4345
0.4357
0.4463 0.4474 0.4564 0.4573 0.4648 0.4656 0.4719 0.4725 0.4778
0.4783
0.4826 0.4830 0.4864 0.4868 0.4896 0.4898 0.4920 0.4922 0.4940
0.4941
0.4955 0.4956 0.4966 0.4967 0.4975 0.4976 0.4982 0.4982 0.4987
0.4987
NORMAL-CURVE AREAS
z 0.00
0.0 0.0000
0.1 0.0398
0.2 0.0793
0.3 0.1179
0.4 0.1554
0.5 0.1915
0.6 0.2257
0.7 0.2580
0.8 0.2881
0.9 0.3159
1.0 0.3413
1.1 0.3643
1.2 0.3849
1.3 0.4032
1.4 0.4192
1.5 0.4332
1.6 0.4452
1.7 0.4554
1.8 0.4641
1.9 0.4713
2.0 0.4772
2.1 0.4821
2.2 0.4861
2.3 0.4893
2.4 0.4918
2.5 0.4938
2.6 0.4953
2.7 0.4965
2.8 0.4974
2.9 0.4981
3.0 0.4987
0.03 0.04
0.0120 0.0160 0.0517 0.0557 0.0910 0.0948 0.1293 0.1331 0.1664
0.1700 0.2019 0.2054
0.2357 0.2389 0.2673 0.2704 0.2967 0.2995 0.3238 0.3264 0.3485
0.3508
0.3708 0.3729 0.3907 0.3925 0.4082 0.4099 0.4236 0.4251 0.4370
0.4382
0.4484 0.4495 0.4582 0.4591 0.4664 0.4671 0.4732 0.4738 0.4788
0.4793
0.4834 0.4838 0.4871 0.4875 0.4901 0.4904 0.4925 0.4927 0.4943
0.4945
0.4957 0.4959 0.4968 0.4969 0.4977 0.4977 0.4983 0.4984 0.4988
0.4988
0.05 0.06 0.07 0.08
0.0199 0.0239 0.0279 0.0319 0.0596 0.0636 0.0675 0.0714 0.0987
0.1026 0.1064 0.1103 0.1368 0.1406 0.1443 0.1480 0.1736 0.1772
0.1808 0.1844 0.2088 0.2123 0.2157 0.2190
0.2422 0.2454 0.2486 0.2517 0.2734 0.2764 0.2794 0.2823 0.3023
0.3051 0.3078 0.3106 0.3289 0.3315 0.3340 0.3365 0.3531 0.3554
0.3577 0.3599
0.3749 0.3770 0.3790 0.3810 0.3944 0.3962 0.3980 0.3997 0.4115
0.4131 0.4147 0.4162 0.4265 0.4279 0.4292 0.4306 0.4394 0.4406
0.4418 0.4429
0.4505 0.4515 0.4525 0.4535 0.4599 0.4608 0.4616 0.4625 0.4678
0.4685 0.4692 0.4699 0.4744 0.4750 0.4756 0.4761 0.4798 0.4803
0.4808 0.4812
0.4842 0.4846 0.4850 0.4854 0.4878 0.4881 0.4884 0.4887 0.4906
0.4909 0.4911 0.4913 0.4929 0.4931 0.4932 0.4934 0.4946 0.4948
0.4949 0.4951
0.4960 0.4961 0.4962 0.4963 0.4970 0.4971 0.4972 0.4973 0.4978
0.4979 0.4979 0.4980 0.4984 0.4985 0.4985 0.4986 0.4989 0.4989
0.4989 0.4990
0.09
0.0359 0.0753 0.1141 0.1517 0.1879 0.2224
0.2549 0.2852 0.3133 0.3389 0.3621
0.3830 0.4015 0.4177 0.4319 0.4441
0.4545 0.4633 0.4706 0.4767 0.4817
0.4857 0.4890 0.4916 0.4936 0.4952
0.4964 0.4974 0.4981 0.4986 0.4990
Also, for z = 4.0, 5.0 and 6.0, the
areas are 0.49997, 0.4999997, and 0.499999999.