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A batch of 3000 inverters from the production line have a mean output voltage of 337.8 V and the Standard deviation of the output voltage is 3.D V (where D is the last two digits of your student number inserted to the right of the decimal point). If the voltages of the produced inverters are assumed to be normally distributed, determine the following: The number of inverters with output voltages greater than 336.9 V. The number of inverters with output voltages less than 337.1 V, The number of inverters with output voltages between 336.2 V and 339.8 V.

A batch of 3000 inverters from the production line have a mean output voltage of 337.8 V and the Standard deviation of the output voltage is 3.D V (where D is the last two digits of your student number inserted to the right of the decimal point). If the voltages of the produced inverters are assumed to be normally distributed, determine the following: The number of inverters with output voltages greater than 336.9 V. The number of inverters with output voltages less than 337.1 V, The number of inverters with output voltages between 336.2 V and 339.8 V.

College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter8: Sequences, Series, And Probability
Section8.CR: Chapter Review
Problem 37E: Find the positive geometric mean between 4 and 64.
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A batch of 3000 inverters from the production line have a mean output voltage of 337.8 V and the Standard deviation of the output voltage is 3.D V (where D is the last two digits of your student number inserted to the right of the decimal point). If the voltages of the produced inverters are assumed to be normally distributed, determine the following:

  1. The number of inverters with output voltages greater than 336.9 V.
  2. The number of inverters with output voltages less than 337.1 V,
  3. The number of inverters with output voltages between 336.2 V and 339.8 V.

 

For this problem you should use the table of z-values shown in Figure below.

I- 01 2 3 4 s 6 7 8 0.0 0.1 0.0000 0.0040 0.0080 0.0120 0.0159 0.0199 0.0239 0.0279 0.0319 0.0359 0.0398 0.0438 0.0478 0.0517 0.0557 0.0596 0.0636 0.0678 0.0714 0.0753 0.2 0.3 0.0793 0.0832 0.0871 0.0910 0.1179 0.1217 0.1255 0.1293 0.1331 0.1554 0.1591 0.1628 0.1664 0.1700 0.1736 0.1772 0.1808 0.1915 0.1950 0.1985 0.2019 0.2054 0.2086 0.2123 0.2157 0.2190 0.2224 0.0948 0.0987 0.1026 0.1064 0.1103 0.1141 0.1388 0.1406 0.1443 0.1480 0.1517 0.1844 0.1879 0.4 0.5 0.6 0.2257 0.2291 0.2324 0.2357 0.2389 0.2422 0.2454 0.2486 0.2517 0.2549 0.7 0.2580 0.2611 0.2642 0.2673 0.2704 0.2734 0.2760 0.2794 0.2823 0.2852 0.2881 0.3159 0.2910 0.2939 0.2967 0.3186 0.3212 0.3238 0.3264 0.3438 0.2995 0.3023 0.3051 0.3289 0.331I5 0.3340 0.3078 0.3106 0.3133 0.3365 0.8 0.9 0.3389 1.0 0.3485 0.3708 0.3729 0.3749 0.3770 0.3790 0.3810 0.3907 0.3925 0.3944 0.3531 0.3413 0.3643 0.3665 0.3849 0.3451 0.3686 0.3508 0.3554 0.3577 0.3599 0.3621 1.1 0.3830 1.2 0.3869 0.3888 0.3962 0.3980 0.3997 0.4015 1.3 14 15 0.4032 0.4049 0.4066 0.4082 0.4099 0.4115 0.4192 0.4332 0.4345 0,4357 0.4370 0,4382 0.4394 0.4131 0,4147 0,4162 04177 0.4292 0.4306 0.4207 0.4222 0.4236 04251 0.4265 0.4279 0.4319 0.4406 0.4418 0.4430 04441 1.6 1.7 0.4452 0.4554 0.4564 0.4573 0.4582 0.4591 0.4641 0.4649 0,4656 0,4664 0.4671 0.4713 0.4474 0.4484 0.4495 0.4505 0.4515 0.4599 4525 0.4535 0.4625 0.4699 0.4545 0.4608 0.4616 0.4633 0.4706 1.8 0.4678 0.4686 0.4693 1.9 0.4719 0.4726 0.4732 0.4738 0.4744 0.4750 0.4756 0.4762 04767 0.4812 0.4817 0.4808 0.4850 0.4854 0.4884 0.4887 2.0 0.4772 0.4778 0.4783 0.4785 0.4793 0.4798 0.4803 2.1 2.2 0.4821 0.4861 0.4893 0.4826 0.4830 0,4834 0.4838 0.4842 0.4846 0.4857 0.4864 0.4868 0.4871 0.4875 0.4878 0.4881 0.4890 2.3 0.4896 0.4898 0.4901 0.4904 0.4906 0.4909 0.4911 0.4913 0.4916 2.4 2.5 0.4920 0.4922 0.4940 0.4941 0.4925 0.4943 0.4945 0.4946 0.4918 0.4927 0.4929 0.4932 0,4934 0.4948 0.4949 0.4951 0.4952 0.4931 0.4936 0.4938 0.4953 0.4955 0.4962 0.4970 0.4971 0.4972 0.4973 0.4979 2.6 0.4956 0.4957 0.4959 0.4960 0.4961 0.4963 0.4964 2.7 0.4965 0.4966 0.4967 0.4968 0.4969 0.4974 0.4975 0.4980 2.8 2.9 0.4974 0.4981 0.4978 0.4982 0.4982 0.4983 0.4984 0.4984 0.4985 0.4985 0.4986 0.4986 0.4976 0.4977 0.4977 0.4980 0.4981 3.0 0.4987 0.4987 0.4987 0.4988 0.4988 0.4989 0.4989 0.4989 0.4990 0.4990 3.1 0.4990 0.4991 0.4991 0.4991 0.4992 0.4992 0.4992 0.4992 0.4993 0.4993 3.2 3.3 0.4993 0.4993 0.4994 0.4995 0.4995 0.4996 0.4994 0,4994 0.4994 0.4994 0.4995 0.4996 0.4996 0.4997 0.4995 0.4995 0.4995 0.4996 0.4996 0.4996 3.4 0.4997 0.4997 0.4997 0.4997 0.4997 0.4997 0.4997 0.4997 0.4997 0.4998 3.5 3.6 3.7 0.4998 0.4998 0.4998 0.4998 0.4998 0.4998 0.4998 0.4998 0.4998 0.4998 0.4998 0.4998 0.4999 0.4999 0.4999 0.4999 0.4999 0.4999 0.4999 0.4999 0.4999 0.4999 0.4999 0.4999 0.4999 0.4999 0.4999 0.4999 0.4999 0.4999 3.8 0.4999 0.4999 0.4999 0.4999 0,4999 0.4999 0.4999 0.4999 0.4999 0,4999 3.9 0.5000 0.5000 0.5000 0.5000 0.5000 0.5000 0.5000 0.5000 0.5000 0.5000 Figure 1: Table of z values for normally distributed curve.
Transcribed Image Text:I- 01 2 3 4 s 6 7 8 0.0 0.1 0.0000 0.0040 0.0080 0.0120 0.0159 0.0199 0.0239 0.0279 0.0319 0.0359 0.0398 0.0438 0.0478 0.0517 0.0557 0.0596 0.0636 0.0678 0.0714 0.0753 0.2 0.3 0.0793 0.0832 0.0871 0.0910 0.1179 0.1217 0.1255 0.1293 0.1331 0.1554 0.1591 0.1628 0.1664 0.1700 0.1736 0.1772 0.1808 0.1915 0.1950 0.1985 0.2019 0.2054 0.2086 0.2123 0.2157 0.2190 0.2224 0.0948 0.0987 0.1026 0.1064 0.1103 0.1141 0.1388 0.1406 0.1443 0.1480 0.1517 0.1844 0.1879 0.4 0.5 0.6 0.2257 0.2291 0.2324 0.2357 0.2389 0.2422 0.2454 0.2486 0.2517 0.2549 0.7 0.2580 0.2611 0.2642 0.2673 0.2704 0.2734 0.2760 0.2794 0.2823 0.2852 0.2881 0.3159 0.2910 0.2939 0.2967 0.3186 0.3212 0.3238 0.3264 0.3438 0.2995 0.3023 0.3051 0.3289 0.331I5 0.3340 0.3078 0.3106 0.3133 0.3365 0.8 0.9 0.3389 1.0 0.3485 0.3708 0.3729 0.3749 0.3770 0.3790 0.3810 0.3907 0.3925 0.3944 0.3531 0.3413 0.3643 0.3665 0.3849 0.3451 0.3686 0.3508 0.3554 0.3577 0.3599 0.3621 1.1 0.3830 1.2 0.3869 0.3888 0.3962 0.3980 0.3997 0.4015 1.3 14 15 0.4032 0.4049 0.4066 0.4082 0.4099 0.4115 0.4192 0.4332 0.4345 0,4357 0.4370 0,4382 0.4394 0.4131 0,4147 0,4162 04177 0.4292 0.4306 0.4207 0.4222 0.4236 04251 0.4265 0.4279 0.4319 0.4406 0.4418 0.4430 04441 1.6 1.7 0.4452 0.4554 0.4564 0.4573 0.4582 0.4591 0.4641 0.4649 0,4656 0,4664 0.4671 0.4713 0.4474 0.4484 0.4495 0.4505 0.4515 0.4599 4525 0.4535 0.4625 0.4699 0.4545 0.4608 0.4616 0.4633 0.4706 1.8 0.4678 0.4686 0.4693 1.9 0.4719 0.4726 0.4732 0.4738 0.4744 0.4750 0.4756 0.4762 04767 0.4812 0.4817 0.4808 0.4850 0.4854 0.4884 0.4887 2.0 0.4772 0.4778 0.4783 0.4785 0.4793 0.4798 0.4803 2.1 2.2 0.4821 0.4861 0.4893 0.4826 0.4830 0,4834 0.4838 0.4842 0.4846 0.4857 0.4864 0.4868 0.4871 0.4875 0.4878 0.4881 0.4890 2.3 0.4896 0.4898 0.4901 0.4904 0.4906 0.4909 0.4911 0.4913 0.4916 2.4 2.5 0.4920 0.4922 0.4940 0.4941 0.4925 0.4943 0.4945 0.4946 0.4918 0.4927 0.4929 0.4932 0,4934 0.4948 0.4949 0.4951 0.4952 0.4931 0.4936 0.4938 0.4953 0.4955 0.4962 0.4970 0.4971 0.4972 0.4973 0.4979 2.6 0.4956 0.4957 0.4959 0.4960 0.4961 0.4963 0.4964 2.7 0.4965 0.4966 0.4967 0.4968 0.4969 0.4974 0.4975 0.4980 2.8 2.9 0.4974 0.4981 0.4978 0.4982 0.4982 0.4983 0.4984 0.4984 0.4985 0.4985 0.4986 0.4986 0.4976 0.4977 0.4977 0.4980 0.4981 3.0 0.4987 0.4987 0.4987 0.4988 0.4988 0.4989 0.4989 0.4989 0.4990 0.4990 3.1 0.4990 0.4991 0.4991 0.4991 0.4992 0.4992 0.4992 0.4992 0.4993 0.4993 3.2 3.3 0.4993 0.4993 0.4994 0.4995 0.4995 0.4996 0.4994 0,4994 0.4994 0.4994 0.4995 0.4996 0.4996 0.4997 0.4995 0.4995 0.4995 0.4996 0.4996 0.4996 3.4 0.4997 0.4997 0.4997 0.4997 0.4997 0.4997 0.4997 0.4997 0.4997 0.4998 3.5 3.6 3.7 0.4998 0.4998 0.4998 0.4998 0.4998 0.4998 0.4998 0.4998 0.4998 0.4998 0.4998 0.4998 0.4999 0.4999 0.4999 0.4999 0.4999 0.4999 0.4999 0.4999 0.4999 0.4999 0.4999 0.4999 0.4999 0.4999 0.4999 0.4999 0.4999 0.4999 3.8 0.4999 0.4999 0.4999 0.4999 0,4999 0.4999 0.4999 0.4999 0.4999 0,4999 3.9 0.5000 0.5000 0.5000 0.5000 0.5000 0.5000 0.5000 0.5000 0.5000 0.5000 Figure 1: Table of z values for normally distributed curve.
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