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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)).

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 22PFA
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do part d) and 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. 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: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)).
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.
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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