A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN: 9780134753119
Author: Sheldon Ross
Publisher: PEARSON
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Estimation
A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.
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1. The top selling Red and Voss tire is rated 70,000 miles, which means nothing. In fact, the distance the tires can run until they wear out is normally distributed random variable with a mean of 82,000 miles and standard deviation of 6400 miles.

a. What is the probability that a tire wears out before 70,000 miles?

b. What is the probability that a tire lasts more than 100,000 miles?

NOTE: Answer the following questions stated above using the Normal Distribution Z table.(attached in the image). Compute and SHOW THE GRAPH of the answers too.

Areas Under the One-Tailed Standard Normal Curve This table provides the area between the meanand some Z score. For example, whenz score = 1.45 0.4265 the area - 0.4265. 145 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.08 0.09 0.0 0.0199 0.0239 0.0000 0.0398 0.0040 0.0080 0.0120 0.0160 0.0279 0.0319 0.0359 0.1 0.0438 0.0478 0.0517 0.0557 0.056 0.0636 0.0987 0.1026 0.0675 0.0714 0.0753 0.0910 0.0832 0.0871 0.1217 0.0948 0.1331 0.1064 0.1443 0.2 0.0793 0.1103 0.1141 0.1255 0.1368 0.1736 0.1772 0.3 0.1480 0.1179 0.1554 0.1293 0.1406 0.1517 0.4 0.1591 0.1628 0.1664 0.1700 0.1808 0.1844 0.1879 0.5 0.1915 0.1900 0.1985 0.2019 D.2054 0.2083 0.2123 0.2157 0.2190 0.2224 0.2422 0.2454 0.2734 0.2764 0.6 0.2257 0.2291 0.2324 0.2357 0.2389 0.2486 0.2517 0.2549 0.2073 0.2967 0.7 0.2580 0.2611 0.2642 D.2704 0.2794 0.2823 0.2852 0.8 0.2881 0.2910 0.2939 0.2995 0.3023 0.3051 0.3078 0.3106 0.3133 0.9 0.3159 0.3180 0.3212 0.3238 0.3264 0.3289 0.3315 0.3340 0.3365 0.3389 1.0 0.3485 0.3413 0.3643 0.3438 0.3461 D.3508 0.3531 0.3554 0.3577 0.3599 0.3621 0.3708 0.3907 1.1 0.3665 0.3686 0.3729 0.3749 0.3770 0.3790 0.3810 0.3830 0.388 0.4066 1.2 0.3849 D.3869 0.3925 0.3944 0.3962 0.3980 0.3997 0.4015 1.3 0.4032 0.4049 0.4082 0.4099 0.4115 0.4131 0.4147 0.4162 0.4177 1.4 0.4192 0.4207 0.4222 0.4236 D.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 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 0.4608 0.4591 0.4671 0.4599 0.4616 0.4625 0.4633 1.3 0.4641 0.4649 0.4656 0.4664 0.4678 0.4686 0.4693 0.4699 0.4706 0.4726 0.4783 0.4830 1.9 0.4713 0.4719 0.4732 0.4738 0.4744 0.4750 0.4756 0.4761 0.4767 2.0 0.4772 0.4778 0.4788 0.4793 0.4798 0.4803 0.4808 0.4812 0.4817 0.4834 0.4842 0.4846 0,4878 2.1 0.4821 0.4361 0.4826 0.4838 0.4850 0.4884 0.4854 0.4857 2.2 0.4804 0.4868 0.4871 0.4875 0.4881 0.4887 0.4890 2.3 0.4893 0.4896 0.4898 0.4901 0.4904 0.4906 0.4909 0.4911 0.4913 0.4916 0.4922 0.4925 0.4943 2.4 0.4918 0.4920 0.4927 0.4929 0.4931 0.4912 0.4934 0.4936 2.5 0.4938 0.4940 0.4941 0.4945 0.4946 0.4948 0.4949 0.4951 0.4952 2.6 0.4953 0.4965 0.4956 0.4960 0.4961 0.4957 0.4968 0.4977 0.4959 0.4962 0,4963 0.4964 2.7 0.4965 0.4966 0.4967 0.4969 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 2.9 0.4981 0.4932 0.4982 0.4983 0.4934 0.4984 0.4985 0.4985 0.4986 0.4986 3.0 0.4987 0.487 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 0.4994 0.4995 0.4993 0.4995 0.4995 0.4995 0.4996 0,4996 0.4997 3.2 0.4993 0.4994 0.4994 0.4994 0.4994 0.4996 0.4996 0.4997 3.3 0.4995 0.4995 0.4996 0.4996 0.4997 3.4 0.4997 0.4997 0.4997 0.4997 0.4997 0.4997 0.4997 0.4998 3.5 0.4998 0.4998 0.4998 0.4998 0.4998 0.4998 0.4998 0.4998 0.4998 0.4998 3.6 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 3.7 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 3.9 0.5000 0.5000 0.5000 0.5000 0.5000 0.5000 0.5000 0.5000 0.5000 0.5000
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Transcribed Image Text:Areas Under the One-Tailed Standard Normal Curve This table provides the area between the meanand some Z score. For example, whenz score = 1.45 0.4265 the area - 0.4265. 145 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.08 0.09 0.0 0.0199 0.0239 0.0000 0.0398 0.0040 0.0080 0.0120 0.0160 0.0279 0.0319 0.0359 0.1 0.0438 0.0478 0.0517 0.0557 0.056 0.0636 0.0987 0.1026 0.0675 0.0714 0.0753 0.0910 0.0832 0.0871 0.1217 0.0948 0.1331 0.1064 0.1443 0.2 0.0793 0.1103 0.1141 0.1255 0.1368 0.1736 0.1772 0.3 0.1480 0.1179 0.1554 0.1293 0.1406 0.1517 0.4 0.1591 0.1628 0.1664 0.1700 0.1808 0.1844 0.1879 0.5 0.1915 0.1900 0.1985 0.2019 D.2054 0.2083 0.2123 0.2157 0.2190 0.2224 0.2422 0.2454 0.2734 0.2764 0.6 0.2257 0.2291 0.2324 0.2357 0.2389 0.2486 0.2517 0.2549 0.2073 0.2967 0.7 0.2580 0.2611 0.2642 D.2704 0.2794 0.2823 0.2852 0.8 0.2881 0.2910 0.2939 0.2995 0.3023 0.3051 0.3078 0.3106 0.3133 0.9 0.3159 0.3180 0.3212 0.3238 0.3264 0.3289 0.3315 0.3340 0.3365 0.3389 1.0 0.3485 0.3413 0.3643 0.3438 0.3461 D.3508 0.3531 0.3554 0.3577 0.3599 0.3621 0.3708 0.3907 1.1 0.3665 0.3686 0.3729 0.3749 0.3770 0.3790 0.3810 0.3830 0.388 0.4066 1.2 0.3849 D.3869 0.3925 0.3944 0.3962 0.3980 0.3997 0.4015 1.3 0.4032 0.4049 0.4082 0.4099 0.4115 0.4131 0.4147 0.4162 0.4177 1.4 0.4192 0.4207 0.4222 0.4236 D.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 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 0.4608 0.4591 0.4671 0.4599 0.4616 0.4625 0.4633 1.3 0.4641 0.4649 0.4656 0.4664 0.4678 0.4686 0.4693 0.4699 0.4706 0.4726 0.4783 0.4830 1.9 0.4713 0.4719 0.4732 0.4738 0.4744 0.4750 0.4756 0.4761 0.4767 2.0 0.4772 0.4778 0.4788 0.4793 0.4798 0.4803 0.4808 0.4812 0.4817 0.4834 0.4842 0.4846 0,4878 2.1 0.4821 0.4361 0.4826 0.4838 0.4850 0.4884 0.4854 0.4857 2.2 0.4804 0.4868 0.4871 0.4875 0.4881 0.4887 0.4890 2.3 0.4893 0.4896 0.4898 0.4901 0.4904 0.4906 0.4909 0.4911 0.4913 0.4916 0.4922 0.4925 0.4943 2.4 0.4918 0.4920 0.4927 0.4929 0.4931 0.4912 0.4934 0.4936 2.5 0.4938 0.4940 0.4941 0.4945 0.4946 0.4948 0.4949 0.4951 0.4952 2.6 0.4953 0.4965 0.4956 0.4960 0.4961 0.4957 0.4968 0.4977 0.4959 0.4962 0,4963 0.4964 2.7 0.4965 0.4966 0.4967 0.4969 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 2.9 0.4981 0.4932 0.4982 0.4983 0.4934 0.4984 0.4985 0.4985 0.4986 0.4986 3.0 0.4987 0.487 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 0.4994 0.4995 0.4993 0.4995 0.4995 0.4995 0.4996 0,4996 0.4997 3.2 0.4993 0.4994 0.4994 0.4994 0.4994 0.4996 0.4996 0.4997 3.3 0.4995 0.4995 0.4996 0.4996 0.4997 3.4 0.4997 0.4997 0.4997 0.4997 0.4997 0.4997 0.4997 0.4998 3.5 0.4998 0.4998 0.4998 0.4998 0.4998 0.4998 0.4998 0.4998 0.4998 0.4998 3.6 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 3.7 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 3.9 0.5000 0.5000 0.5000 0.5000 0.5000 0.5000 0.5000 0.5000 0.5000 0.5000
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