Complete the assignment:
Q1: An economist wishes to estimate the average family income in a certain population. The population standard deviation is known to be $4,500, and the economist uses a random sample of size = 225.
a. What is the probability that the sample mean will fall within $800 of the population mean?
Explain how you get from P(Z<8/3) - P(Z<-8/3) to 0.9962 - 0.0038? How do you check the z-table to find these values?
Please show me in the Example Z-Table below.
b. What is the probability that the sample mean will exceed the population mean by more than $600.
Explain to me how you get from 1-P(Z<2) to 1-0.9772 to 0.0278 in detail? Should 0.0278 really equal 0.0228? Please show me in the Example Z-Table below.
Q2: The article "Reliability of Domestic Waste Biofilm Reactors" (J. of Envir. Engr., 1995: 785-790) suggests that substrate concentration (mg/cm^3) of influent to a reactor is normally distributed with μ= 0.30 and σ= 0.06.
a. What is the probability that the concentration exceeds 0.40? Same question as above, how do you find 0.9525 from the z-tables? Please show me in the Example Z-Table below.
b. What is the probability that the concentration is at most 0.25? Same question as above, how do you find P(Z<= -5/6) from the z-tables? Please show me in the Example Z-Table below.
c. How would you characterize the largest 10% of all concentration levels? Please show me in the z-table below where you found these values? Please show me in the Example Z-Table below.
Example Z-Table
|
z
|
0
|
0.01
|
0.02
|
0.03
|
0.04
|
0.05
|
0.06
|
0.07
|
0.08
|
0.09
|
|
0
|
0
|
0.004
|
0.008
|
0.012
|
0.016
|
0.0199
|
0.0239
|
0.0279
|
0.0319
|
0.0359
|
|
0.1
|
0.0398
|
0.0438
|
0.0478
|
0.0517
|
0.0557
|
0.0596
|
0.0636
|
0.0675
|
0.0714
|
0.0753
|
|
0.2
|
0.0793
|
0.0832
|
0.0871
|
0.091
|
0.0948
|
0.0987
|
0.1026
|
0.1064
|
0.1103
|
0.1141
|
|
0.3
|
0.1179
|
0.1217
|
0.1255
|
0.1293
|
0.1331
|
0.1368
|
0.1406
|
0.1443
|
0.148
|
0.1517
|
|
0.4
|
0.1554
|
0.1591
|
0.1628
|
0.1664
|
0.17
|
0.1736
|
0.1772
|
0.1808
|
0.1844
|
0.1879
|
|
0.5
|
0.1915
|
0.195
|
0.1985
|
0.2019
|
0.2054
|
0.2088
|
0.2123
|
0.2157
|
0.219
|
0.2224
|
|
0.6
|
0.2257
|
0.2291
|
0.2324
|
0.2357
|
0.2389
|
0.2422
|
0.2454
|
0.2486
|
0.2517
|
0.2549
|
|
0.7
|
0.258
|
0.2611
|
0.2642
|
0.2673
|
0.2704
|
0.2734
|
0.2764
|
0.2794
|
0.2823
|
0.2852
|
|
0.8
|
0.2881
|
0.291
|
0.2939
|
0.2967
|
0.2995
|
0.3023
|
0.3051
|
0.3078
|
0.3106
|
0.3133
|
|
0.9
|
0.3159
|
0.3186
|
0.3212
|
0.3238
|
0.3264
|
0.3289
|
0.3315
|
0.334
|
0.3365
|
0.3389
|
|
1
|
0.3413
|
0.3438
|
0.3461
|
0.3485
|
0.3508
|
0.3531
|
0.3554
|
0.3577
|
0.3599
|
0.3621
|
|
1.1
|
0.3643
|
0.3665
|
0.3686
|
0.3708
|
0.3729
|
0.3749
|
0.377
|
0.379
|
0.381
|
0.383
|
|
1.2
|
0.3849
|
0.3869
|
0.3888
|
0.3907
|
0.3925
|
0.3944
|
0.3962
|
0.398
|
0.3997
|
0.4015
|
|
1.3
|
0.4032
|
0.4049
|
0.4066
|
0.4082
|
0.4099
|
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
|
0.437
|
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
|
0.4591
|
0.4599
|
0.4608
|
0.4616
|
0.4625
|
0.4633
|
|
1.8
|
0.4641
|
0.4649
|
0.4656
|
0.4664
|
0.4671
|
0.4678
|
0.4686
|
0.4693
|
0.4699
|
0.4706
|
|
1.9
|
0.4713
|
0.4719
|
0.4726
|
0.4732
|
0.4738
|
0.4744
|
0.475
|
0.4756
|
0.4761
|
0.4767
|
|
2
|
0.4772
|
0.4778
|
0.4783
|
0.4788
|
0.4793
|
0.4798
|
0.4803
|
0.4808
|
0.4812
|
0.4817
|
|
2.1
|
0.4821
|
0.4826
|
0.483
|
0.4834
|
0.4838
|
0.4842
|
0.4846
|
0.485
|
0.4854
|
0.4857
|
|
2.2
|
0.4861
|
0.4864
|
0.4868
|
0.4871
|
0.4875
|
0.4878
|
0.4881
|
0.4884
|
0.4887
|
0.489
|
|
2.3
|
0.4893
|
0.4896
|
0.4898
|
0.4901
|
0.4904
|
0.4906
|
0.4909
|
0.4911
|
0.4913
|
0.4916
|
|
2.4
|
0.4918
|
0.492
|
0.4922
|
0.4925
|
0.4927
|
0.4929
|
0.4931
|
0.4932
|
0.4934
|
0.4936
|
|
2.5
|
0.4938
|
0.494
|
0.4941
|
0.4943
|
0.4945
|
0.4946
|
0.4948
|
0.4949
|
0.4951
|
0.4952
|
|
2.6
|
0.4953
|
0.4955
|
0.4956
|
0.4957
|
0.4959
|
0.496
|
0.4961
|
0.4962
|
0.4963
|
0.4964
|
|
2.7
|
0.4965
|
0.4966
|
0.4967
|
0.4968
|
0.4969
|
0.497
|
0.4971
|
0.4972
|
0.4973
|
0.4974
|
|
2.8
|
0.4974
|
0.4975
|
0.4976
|
0.4977
|
0.4977
|
0.4978
|
0.4979
|
0.4979
|
0.498
|
0.4981
|
|
2.9
|
0.4981
|
0.4982
|
0.4982
|
0.4983
|
0.4984
|
0.4984
|
0.4985
|
0.4985
|
0.4986
|
0.4986
|
|
3
|
0.4987
|
0.4987
|
0.4987
|
0.4988
|
0.4988
|
0.4989
|
0.4989
|
0.4989
|
0.499
|
0.499
|
|
3.1
|
0.499
|
0.4991
|
0.4991
|
0.4991
|
0.4992
|
0.4992
|
0.4992
|
0.4992
|
0.4993
|
0.4993
|
|
3.2
|
0.4993
|
0.4993
|
0.4994
|
0.4994
|
0.4994
|
0.4994
|
0.4994
|
0.4995
|
0.4995
|
0.4995
|
|
3.3
|
0.4995
|
0.4995
|
0.4995
|
0.4996
|
0.4996
|
0.4996
|
0.4996
|
0.4996
|
0.4996
|
0.4997
|
|
3.4
|
0.4997
|
0.4997
|
0.4997
|
0.4997
|
0.4997
|
0.4997
|
0.4997
|
0.4997
|
0.4997
|
0.4998
|