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? Kindly SOLVE the problems using the Normal Distribtion Z Table (attached in the image) and SHOW THE GRAPH too, thanks.
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? Kindly SOLVE the problems using the Normal Distribtion Z Table (attached in the image) and SHOW THE GRAPH too, thanks.
A First Course in Probability (10th Edition)
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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
a. What is the
b. What is the probability that a tire lasts more than 100,000 miles?
Kindly SOLVE the problems using the Normal Distribtion Z Table (attached in the image) and SHOW THE GRAPH too, thanks.
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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