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. Areas Under the One-Tailed Standard Normal CurveThis table provides the area betweenthe meanand some Z score.For example, whenz score = 1.450.4265the area - 0.4265.1450.000.010.020.030.040.050.060.080.090.00.0199 0.02390.00000.03980.00400.00800.01200.01600.02790.03190.03590.10.04380.04780.05170.05570.0560.06360.0987 0.10260.06750.07140.07530.09100.0832 0.08710.12170.09480.13310.10640.14430.20.07930.11030.11410.12550.13680.1736 0.17720.30.14800.11790.15540.12930.14060.15170.40.15910.16280.16640.17000.18080.18440.18790.50.19150.19000.19850.2019D.20540.20830.21230.21570.21900.22240.2422 0.24540.2734 0.27640.60.22570.22910.23240.23570.23890.24860.25170.25490.20730.29670.70.25800.26110.2642D.27040.27940.28230.28520.80.28810.29100.29390.29950.30230.30510.3078 0.31060.31330.90.31590.31800.32120.32380.32640.32890.33150.33400.33650.33891.00.34850.34130.36430.34380.3461D.35080.35310.35540.35770.35990.36210.37080.39071.10.36650.36860.37290.3749 0.37700.37900.38100.38300.3880.40661.20.3849D.38690.39250.39440.39620.39800.39970.40151.30.40320.40490.40820.40990.41150.41310.41470.41620.41771.40.41920.42070.42220.4236D.42510.42650.42790.42920.43060.43191.50.43320.43450.43570.43700.43820.43940.44060.44180.44290.44411.60.44520.44630.44740.44840.44950,45050.45150.45250.45350.45451.70.45540.45640.45730.45820.46080.45910.46710.45990.46160.46250.46331.30.46410.46490.46560.46640.46780.46860.46930.46990.47060.47260.47830.48301.90.47130.47190.47320.47380.47440.47500.47560.47610.47672.00.47720.47780.47880.47930.47980.48030.48080.48120.48170.48340.4842 0.48460,48782.10.48210.43610.48260.48380.48500.48840.48540.48572.20.48040.48680.48710.48750.48810.48870.48902.30.48930.48960.48980.49010.49040.49060.49090.49110.49130.49160.49220.49250.49432.40.49180.49200.49270.49290.49310.49120.49340.49362.50.49380.49400.49410.49450.49460.49480.49490.49510.49522.60.49530.49650.49560.4960 0.49610.49570.49680.49770.49590.49620,4963 0.49642.70.49650.49660.49670.49690.49700.49710.49720.49730.49742.80.49740.49750.49760.49770.49780.49790.49790.49800.49812.90.49810.49320.49820.49830.49340.49840.49850.49850.49860.49863.00.49870.4870.49870.49880.49880.4989 0.49890.49890.49900.49903.10.49900.49910.49910.49910.49920.49920.49920.49920.49930.49930.49940.49950.49930.49950.4995 0.49950.4996 0,49960.49973.20.49930.49940.49940.49940.49940.4996 0.49960.49973.30.49950.49950.49960.49960.49973.40.49970.49970.49970.49970.49970.49970.49970.49983.50.49980.49980.49980.49980.49980.49980.49980.49980.49980.49983.60.49980.49980.49990.49990.49990.49990.49990.49990.49990.49990.49990.4999 0.49990.49993.70.49990.49990.49990.49990.49990.4999 0.49993.80.49990.49990.49990.49990.49990.49990.49990.49990.49993.90.5000 0.50000.50000.50000.50000.50000.50000.50000.50000.5000

Standard normal score: The standard normal score follows normal distribution with mean 0 and…

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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 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.

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

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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