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The results of a nationwide aptitude test in mathematics are normally distributed with m=80 and s=10. Find the raw score such that 80% cases are below it. Solve the following by concept of normal distribution and graph clearly. Show your complete solution and write clearly and readable.

The results of a nationwide aptitude test in mathematics are normally distributed with m=80 and s=10. Find the raw score such that 80% cases are below it. Solve the following by concept of normal distribution and graph clearly. Show your complete solution and write clearly and readable.

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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The results of a nationwide aptitude test in mathematics are normally distributed with m=80 and s=10. Find the raw score such that 80% cases are below it. Solve the following by concept of normal distribution and graph clearly. Show your complete solution and write clearly and readable. Thank you.
STANDARD NORMAL TABLE (Z) Entries in the table give the area under the curve between the mean and z standard deviations above the mean. For example, for z = 1.25 the area under the curve between the mean (0) and z is 0.3944. 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.0 0.0000 0.0040 0.0080 0.0120 0.0160 0.0190 0.0239 0.0279 0.0319 0.0359 0.0398 0.2 0.0793 0.3 0.1179 0.4 0.1554 0.1 0.0478 0.0517 0.0557 0.0871 0.1255 0.0438 0.0596 0.0636 0.0675 0.0714 0.0753 0.1103 0.1480 0.0832 0.0910 0.0948 0.0987 0.1026 0.1064 0.1141 0.1217 0.1293 0.1331 0.1368 0.1406 0.1443 0.1517 0.1700 0.2054 0.1879 0.2224 0.1591 0.1628 0.1664 0.1736 0.1772 0.1808 0.1844 0.5 0.1915 0.1950 0.1985 0.2019 0.2088 0.2123 0.2157 0.2190 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 0.2764 0.2794 0.2823 0.2852 0.8 0.2881 0.2910 0.2939 0.2969 0.2995 0.3023 0.3051 0.3078 0.3106 0.3133 0.9 1.0 0.3212 0.3238 0.3264 0.3461 0.3686 0.3186 0.3289 0.3340 0.3365 0.3389 0.3529 0.3159 0.3315 0.3413 0.3438 0.3485 0.3508 0.3513 0.3554 0.3577 0.3621 1.1 1.2 1.3 0.3643 0.3665 0.3708 0.3729 0.3749 0.3770 0.3790 0.3810 0.3830 0.3849 0.3869 0.3907 0.4082 0.4099 0.3888 0.3925 0.3944 0.3962 0.3980 0.3997 0.4015 0.4032 0.4049 0.4066 0.4115 0.4131 0.4147 0.4162 0.4177 1.4 0.4192 0.4207 0.4222 0.4236 0.4251 0.4265 0.4279 0.4292 0.4306 0.4319 1.5 0.4332 0.4345 0.4357 0.4370 0.4382 0.4394 0.4406 0.4418 0.4429 0.4441 1.6 1.7 1.8 0.4452 0.4463 0.4474 0.4484 0.4495 0.4505 0.4515 0.4525 0.4535 0.4545 0.4554 0.4641 0.4564 0.4573 0.4582 0.4591 0.4599 0.4608 0.4616 0.4625 0.4633 0.4649 0.4656 0.4664 0.4671 0.4678 0.4686 0.4693 0.4699 0.4706 1.9 2.0 0.4772 2.1 2.2 0.4861 0.4719 0.4778 0.4713 0.4726 0.4732 0.4738 0.4744 0.4750 0.4756 0.4761 0.4767 0.4783 0.4788 0.4793 0.4798 0.4842 0.4803 0.4808 0.4812 0.4817 0.4838 0.4875 0.4821 0.4826 0.4830 0.4834 0.4846 0.4850 0.4854 0.4857 0.4864 0.4868 0.4871 0.4878 0.4881 0.4884 0.4887 0.4890 2.3 2.4 2.5 0.4893 0.4918 0.4896 0.4898 0.4901 0.4904 0.4906 0.4909 0.4911 0.4913 0.4916 0.4920 0.4922 0.4925 0.4927 0.4929 0.4931 0.4932 0.4934 0.4936 0.4938 0.4953 0.4965 0.4941 0.4956 0.4940 0.4945 0.4959 0.4943 0.4946 0.4948 0.4949 0.4951 0.4952 2.6 0.4955 0.4966 0.4975 0.4957 0.4960 0.4961 0.4962 0.4963 0.4964 2.7 0.4967 0.4968 0.4969 0.4970 0.4971 0.4972 0.4973 0.4974 2.8 2.9 3.0 3.1 3.2 3.3 0.4995 3.4 0.4997 0.4974 0.4976 0.4977 0.4977 0.4978 0.4979 0.4979 0.4980 0.4981 0.4981 0.4982 0.4982 0.4983 0.4984 0.4984 0.4985 0.4985 0.4986 0.4986 0.4987 0.4987 0.4987 0.4988 0.4988 0.4989 0.4989 0.4989 0.4990 0.4990 0.4991 0.4991 0.4992 0.4994 0.4994 0.4990 0.4991 0.4992 0.4992 0.4992 0.4993 0.4993 0.4993 0.4995 0.4993 0.4994 0.4994 0.4994 0.4995 0.4995 0.4995 0.4995 0.4996 0.4996 0.4996 0.4996 0.4996 0.4996 0.4997 0.4997 0.4997 0.4997 0.4997 0.4997 0.4997 0.4997 0.4997 0.4998
Transcribed Image Text:STANDARD NORMAL TABLE (Z) Entries in the table give the area under the curve between the mean and z standard deviations above the mean. For example, for z = 1.25 the area under the curve between the mean (0) and z is 0.3944. 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.0 0.0000 0.0040 0.0080 0.0120 0.0160 0.0190 0.0239 0.0279 0.0319 0.0359 0.0398 0.2 0.0793 0.3 0.1179 0.4 0.1554 0.1 0.0478 0.0517 0.0557 0.0871 0.1255 0.0438 0.0596 0.0636 0.0675 0.0714 0.0753 0.1103 0.1480 0.0832 0.0910 0.0948 0.0987 0.1026 0.1064 0.1141 0.1217 0.1293 0.1331 0.1368 0.1406 0.1443 0.1517 0.1700 0.2054 0.1879 0.2224 0.1591 0.1628 0.1664 0.1736 0.1772 0.1808 0.1844 0.5 0.1915 0.1950 0.1985 0.2019 0.2088 0.2123 0.2157 0.2190 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 0.2764 0.2794 0.2823 0.2852 0.8 0.2881 0.2910 0.2939 0.2969 0.2995 0.3023 0.3051 0.3078 0.3106 0.3133 0.9 1.0 0.3212 0.3238 0.3264 0.3461 0.3686 0.3186 0.3289 0.3340 0.3365 0.3389 0.3529 0.3159 0.3315 0.3413 0.3438 0.3485 0.3508 0.3513 0.3554 0.3577 0.3621 1.1 1.2 1.3 0.3643 0.3665 0.3708 0.3729 0.3749 0.3770 0.3790 0.3810 0.3830 0.3849 0.3869 0.3907 0.4082 0.4099 0.3888 0.3925 0.3944 0.3962 0.3980 0.3997 0.4015 0.4032 0.4049 0.4066 0.4115 0.4131 0.4147 0.4162 0.4177 1.4 0.4192 0.4207 0.4222 0.4236 0.4251 0.4265 0.4279 0.4292 0.4306 0.4319 1.5 0.4332 0.4345 0.4357 0.4370 0.4382 0.4394 0.4406 0.4418 0.4429 0.4441 1.6 1.7 1.8 0.4452 0.4463 0.4474 0.4484 0.4495 0.4505 0.4515 0.4525 0.4535 0.4545 0.4554 0.4641 0.4564 0.4573 0.4582 0.4591 0.4599 0.4608 0.4616 0.4625 0.4633 0.4649 0.4656 0.4664 0.4671 0.4678 0.4686 0.4693 0.4699 0.4706 1.9 2.0 0.4772 2.1 2.2 0.4861 0.4719 0.4778 0.4713 0.4726 0.4732 0.4738 0.4744 0.4750 0.4756 0.4761 0.4767 0.4783 0.4788 0.4793 0.4798 0.4842 0.4803 0.4808 0.4812 0.4817 0.4838 0.4875 0.4821 0.4826 0.4830 0.4834 0.4846 0.4850 0.4854 0.4857 0.4864 0.4868 0.4871 0.4878 0.4881 0.4884 0.4887 0.4890 2.3 2.4 2.5 0.4893 0.4918 0.4896 0.4898 0.4901 0.4904 0.4906 0.4909 0.4911 0.4913 0.4916 0.4920 0.4922 0.4925 0.4927 0.4929 0.4931 0.4932 0.4934 0.4936 0.4938 0.4953 0.4965 0.4941 0.4956 0.4940 0.4945 0.4959 0.4943 0.4946 0.4948 0.4949 0.4951 0.4952 2.6 0.4955 0.4966 0.4975 0.4957 0.4960 0.4961 0.4962 0.4963 0.4964 2.7 0.4967 0.4968 0.4969 0.4970 0.4971 0.4972 0.4973 0.4974 2.8 2.9 3.0 3.1 3.2 3.3 0.4995 3.4 0.4997 0.4974 0.4976 0.4977 0.4977 0.4978 0.4979 0.4979 0.4980 0.4981 0.4981 0.4982 0.4982 0.4983 0.4984 0.4984 0.4985 0.4985 0.4986 0.4986 0.4987 0.4987 0.4987 0.4988 0.4988 0.4989 0.4989 0.4989 0.4990 0.4990 0.4991 0.4991 0.4992 0.4994 0.4994 0.4990 0.4991 0.4992 0.4992 0.4992 0.4993 0.4993 0.4993 0.4995 0.4993 0.4994 0.4994 0.4994 0.4995 0.4995 0.4995 0.4995 0.4996 0.4996 0.4996 0.4996 0.4996 0.4996 0.4997 0.4997 0.4997 0.4997 0.4997 0.4997 0.4997 0.4997 0.4997 0.4998
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