Make a decision. A machine used to fill a gallon-sized paint can is regulated so that the amount of paint dispensed has a mean of 128 ounces and a standard deviation of 0.2 ounces. You randomly select 40 cans and carefully measure the contents. The sample mean of the cans is 127.9 ounces.Does the machine need to be reset? Explain your reasoning and show your work. [Use algebra and Table A2] NEGATIVE z ScoresTABLE A-2 Standard Normal (z) Distribution: Cumulative Area from the LEFT.00.01.02.03.04.05.06.07.08.09-3.50 andlower.0001-3.4.0003.0003.0003.0003.0003.0003.0003.0003.0003.0002-3.3.0005.0005.0005.0004.0004.0004.0004.0004.0004.0003-3.2.0007.0007.0006.0006.0006.0006.0006.0005.0005.0005-3.1.0010.0009.00090009.0008.0008.0008.0008.0007.0007-3.0.0013.0013.0013.0012.0012.0011.0011.0011.0010.0010-2.9.0019.0018.0018.0017.0016.0016.0015.0015.0014.0014-2.8.0026.0025.0024.0023.0023.0022.0021.0021.0020.0019-2.7.0035.0034.0033.0032.0031.0030.0029.0028.0027.0026-2.6.0047.0045.0044.0043.0041.0040.0039.0038.0037.0036-2.5.0062.0060.0059.00570055.0054.0052.0051.0049.0048-2.4.0082.0080.0078.0075.0073.0071.0069.0068.0066.0064-2.3.0107.0104.0102,0099.0096.0094.0091.0089.0087.0084-2.2.0139.01360132.01290125.0122.0119.0116.0113.0110-2.1.0179.0174.0170.0166.0162.0158.0154.0150.0146.0143-2.0.0228.0222.0217.0212.0207.0202.0197.0192.0188.0183-1.9.0287.0281.0274.0268.0262.0256.0250.0244.0239.0233-1.8.0359.0351.0344.0336.0329.0322.0314.0307.0301.0294-1.7.0446.0436.0427.0418.0409.0401.0392.0384.0375.0367-1.6.0548.0537.0526.0516.0505.0495.0485.0475.0465.0455-1.5.0668.0655.0643.0630.0618.0606.0594.0582.0571.0559-1.4.0808.0793.0778.0764.0749.0735.0721.0708.0694.0681-1.3.0968.0951.0934.0918.0901.0885.0869.0853.0838.0823-1.2.1151.1131.1112.1093.1075.1056.1038.1020.1003.0985-1.1.1357.1335.1314.1292.1271.1251.1230.1210.1190.1170-1.0.1587.1562.1539.1515.1492.14691446.1423.1401.1379-0.91841.1814.1788.1762.1736.1711.1685.1660.16351611-0.8.2119.2090.2061.2033.2005.1977.1949.1922.1894.1867-0.7.2420.2389.2358.2327.2296.2266.2236.2206.2177.2148-0.6.27432709.2676.2643.26112578.2546.2514.2483.2451-0.5.3085.3050.3015.298129462912.2877.2843.2810.2776-0.43446.3409.3372.3336.3300326432283192.31563121-0.3.38213783.3745.3707.3669.3632.3594.355735203483-0.2.4207.4168.41294090.4052.4013.3974.3936.3897.3859-0.1.4602.4562.4522.4483.44434404.4364.4325.4286.4247-0.0.5000.4960.4920.4880484048014761.472146814641NOTE: For values of z below –3.49, use 0.0001 for the area.(continued)*Use these common values that result from interpolation:z ScoreArea-1.6450.0500-2.5750.0050N

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Description: Make a decision. A machine used to fill a gallon-sized paint can is regulated so that the amount of paint dispensed has a mean of 128 ounces and a standard deviation of 0.2 ounces. You randomly select 40 cans and carefully measure the contents. The s

the given values are population mean = μ =128 the population standard deviation = σ = 0.2 The sample…

Answered: Make a decision. A machine used to fill…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Make a decision. A machine used to fill a gallon-sized paint can is regulated so that the amount of paint dispensed has a mean of 128 ounces and a standard deviation of 0.2 ounces. You randomly select 40 cans and carefully measure the contents. The sample mean of the cans is 127.9 ounces.

Does the machine need to be reset? Explain your reasoning and show your work. [Use algebra and Table A2]

NEGATIVE z Scores
TABLE A-2 Standard Normal (z) Distribution: Cumulative Area from the LEFT
.00
.01
.02
.03
.04
.05
.06
.07
.08
.09
-3.50 and
lower
.0001
-3.4
.0003
.0003
.0003
.0003
.0003
.0003
.0003
.0003
.0003
.0002
-3.3
.0005
.0005
.0005
.0004
.0004
.0004
.0004
.0004
.0004
.0003
-3.2
.0007
.0007
.0006
.0006
.0006
.0006
.0006
.0005
.0005
.0005
-3.1
.0010
.0009
.0009
0009
.0008
.0008
.0008
.0008
.0007
.0007
-3.0
.0013
.0013
.0013
.0012
.0012
.0011
.0011
.0011
.0010
.0010
-2.9
.0019
.0018
.0018
.0017
.0016
.0016
.0015
.0015
.0014
.0014
-2.8
.0026
.0025
.0024
.0023
.0023
.0022
.0021
.0021
.0020
.0019
-2.7
.0035
.0034
.0033
.0032
.0031
.0030
.0029
.0028
.0027
.0026
-2.6
.0047
.0045
.0044
.0043
.0041
.0040
.0039
.0038
.0037
.0036
-2.5
.0062
.0060
.0059
.0057
0055
.0054
.0052
.0051
.0049
.0048
-2.4
.0082
.0080
.0078
.0075
.0073
.0071
.0069
.0068
.0066
.0064
-2.3
.0107
.0104
.0102
,0099
.0096
.0094
.0091
.0089
.0087
.0084
-2.2
.0139
.0136
0132
.0129
0125
.0122
.0119
.0116
.0113
.0110
-2.1
.0179
.0174
.0170
.0166
.0162
.0158
.0154
.0150
.0146
.0143
-2.0
.0228
.0222
.0217
.0212
.0207
.0202
.0197
.0192
.0188
.0183
-1.9
.0287
.0281
.0274
.0268
.0262
.0256
.0250
.0244
.0239
.0233
-1.8
.0359
.0351
.0344
.0336
.0329
.0322
.0314
.0307
.0301
.0294
-1.7
.0446
.0436
.0427
.0418
.0409
.0401
.0392
.0384
.0375
.0367
-1.6
.0548
.0537
.0526
.0516
.0505
.0495
.0485
.0475
.0465
.0455
-1.5
.0668
.0655
.0643
.0630
.0618
.0606
.0594
.0582
.0571
.0559
-1.4
.0808
.0793
.0778
.0764
.0749
.0735
.0721
.0708
.0694
.0681
-1.3
.0968
.0951
.0934
.0918
.0901
.0885
.0869
.0853
.0838
.0823
-1.2
.1151
.1131
.1112
.1093
.1075
.1056
.1038
.1020
.1003
.0985
-1.1
.1357
.1335
.1314
.1292
.1271
.1251
.1230
.1210
.1190
.1170
-1.0
.1587
.1562
.1539
.1515
.1492
.1469
1446
.1423
.1401
.1379
-0.9
1841
.1814
.1788
.1762
.1736
.1711
.1685
.1660
.1635
1611
-0.8
.2119
.2090
.2061
.2033
.2005
.1977
.1949
.1922
.1894
.1867
-0.7
.2420
.2389
.2358
.2327
.2296
.2266
.2236
.2206
.2177
.2148
-0.6
.2743
2709
.2676
.2643
.2611
2578
.2546
.2514
.2483
.2451
-0.5
.3085
.3050
.3015
.2981
2946
2912
.2877
.2843
.2810
.2776
-0.4
3446
.3409
.3372
.3336
.3300
3264
3228
3192
.3156
3121
-0.3
.3821
3783
.3745
.3707
.3669
.3632
.3594
.3557
3520
3483
-0.2
.4207
.4168
.4129
4090
.4052
.4013
.3974
.3936
.3897
.3859
-0.1
.4602
.4562
.4522
.4483
.4443
4404
.4364
.4325
.4286
.4247
-0.0
.5000
.4960
.4920
.4880
4840
4801
4761
.4721
4681
4641
NOTE: For values of z below –3.49, use 0.0001 for the area.
(continued)
*Use these common values that result from interpolation:
z Score
Area
-1.645
0.0500
-2.575
0.0050
N

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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