As an engineer working for a water bottling company, you collect the following data in order to test the performance of the bottling systems. Assume the normal distributio Milliliters of Water in the Bottle Frequency 485 490 milliliters 495 500 505 510 515 What is the mean (in milliliters)? milliliters What is the standard deviation (in milliliters)? What is the z value corresponding to 495 milliliters? z = Referring to this table, determine the A value. A = 8 12 22 35 20 13 12 Determine the probability that a bottle would be filled with more than 495 milliliters. probability=

Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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As an engineer working for a water bottling company, you collect the following data in order to test the performance of the bottling systems. Assume the normal distribution
Milliliters of Water in the Bottle
485
490
milliliters
495
500
505
510
515
What is the mean (in milliliters)?
milliliters
What is the standard deviation (in milliliters)?
Frequency
What is the z value corresponding to 495 milliliters?
Z =
Referring to this table, determine the A value.
A =
8
12
22
35
20
13
12
Determine the probability that a bottle would be filled with more than 495 milliliters.
probability =
Transcribed Image Text:As an engineer working for a water bottling company, you collect the following data in order to test the performance of the bottling systems. Assume the normal distribution Milliliters of Water in the Bottle 485 490 milliliters 495 500 505 510 515 What is the mean (in milliliters)? milliliters What is the standard deviation (in milliliters)? Frequency What is the z value corresponding to 495 milliliters? Z = Referring to this table, determine the A value. A = 8 12 22 35 20 13 12 Determine the probability that a bottle would be filled with more than 495 milliliters. probability =
Areas Under the Standard Normal Curve-The Values Were Generated Using the Standard Normal
Distribution Function of Excel
Note that the standard normal curve is symmetrical about the mean.
z
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.1
0.11
0.12
Mean - 0
A
0.0000
0.0040
0.0080
0.0120
0.0160
0.0199
0.0239
0.0279
0.0319
0.0359
0.0398
0.0438
0.0478
z
Z
0.13
0.14
0.15
0.16
0.17
0.18
0.19
0.2
0,21
0.22
0.23
0.24
0.25
A
0.0517
0.0557
0.0596
0.0636
0.0675
0.0714
0.0753
0.0793
0.0832
0.0871
0.0910
0.0948
0.0987
Z
0.26
0.27
0.28
0.29
0.3
0.31
0.32
0.33
0.34
0.35
0.36
0.37
0.38
A03413
2 = 1.00
A
0.1026
0.1064
0.1103
0.1141
0.1179
0.1217
0.1255
0.1293
0.1331
0.1368
0.1406
0.1443
0.1480
z
0.39
0.4
0.41
0.42
0.43
0.44
0.45
0.46
0.47
0.48
0.49
0.5
0.51
A
0.1517
0.1554
0.1591
0.1628
0.1664
0.1700
0.1736
0.1772
0.1808
0.1844
0.1879
0.1915
0.1950
z
0.52
0.53
0.54
0.55
0.56
0.57
0.58
0.59
0.6
0.61
0.62
0.63
0.64
A-0.4772
22.00
A
0.1985
0.2019
0.2054
0.2088
0.2123
0.2157
0.2190
0.2224
0.2257
0.2291
0.2324
0.2357
0.2389
z
0.65
0.66
0.67
0.68
0.69
0.7
0.71
0.72
0.73
0.74
0.75
0.76
0.77
A
z
0.2422 0.78
0.2454 0.79
0.2486
0.2517 0.81
0.2549 0.82
0.2580 0.83
0.2611 0.84
0.2642 0.85
0.2673 0.86
0.2704 0.87
0.2734 0.88
0.2764 0.89
0.2794
0.9
A-0.4987
0.8
23.00
0.2823
0.2852
0.2881
0.2910
0.2939
0.2967
0.2995
0.3023
0.3051
0.3078
0.3106
0.3133
0.3159
Areas Under the Standard Normal Curve-The Values Were Generated Using the Standard Normal
Distribution Function of Excel (continued)
z
1.1
0.3186
0.3212
0.3238
1.11
0.3264
0.3289
0.3315
z
0.91
0.92
0.93
0.94
0.95
0.96
0.97
0.98
0.99
1
1.01
1.02
1.03
1.04
1.05
1.06
1.07
1.18
1.19
A
z
A
0.3643 1.29 0.4015
0.3665
0.4032
0.3686
0.4049
1.13 0.3708 1.32 0.4066
1.14 0.3729 1.33 0.4082
1.15 0.3749 1.34 0.4099
1.16 0.3770 1.35 0.4115
1.17 0.3790 1.36 0.4131
0.3810 1.37 0.4147
0.3830 1.38 0.4162
1.2 0.3849 1.39 0.4177
1.21 0.3869 1.4
0.4192
1.41
0.4207
1.22 0.3888
1.23 0.3907 1.42 0.4222
1.24 0.3925 1.43 0.4236
1.25 0.3944 1.44 0.4251
1.26 0.3962 1.45 0.4265
1.27 0.3980 1.46 0.4279
1.28 0.3997 1.47 0.4292
0.3340
0.3365
0.3389
0.3413
0.3438
0.3461
0.3485
0.3508
0.3531
0.3554
0.3577
0.3599
1.08
1.09 0.3621
2.28
ATAU
in 20
2.29
22
2.3
and
444
2.31
And
444
2.32
444
2.33
2.34
B
2.25
2.35
4:DD
2.36
2.37
2.38
2.39
2.4
2.41
2.42
0.4878
0.4881
0:4001
O ARRA
0.4884
0.4887
0.Your
0 4900
0.4890
0.4893
0.1000
Areas Under the Standard Normal Curve-The Values Were Generated Using the Standard Normal
Distribution Function of Excel (continued)
0.4875 2.43
2.24
2.25
2.26
2.44
2.45
222
2.27
2.46
247
2.47
0.1006
0.4896
0 4899
0.4898
0.1000
0.4001
0.4901
04904
0.4904
1.12
0.4906
0.7500
0.4909
0.4911
wayan
0.4913
0.4916
0.4918
0.4920
0.4922
2.48
2.49
26
2.5
3
2.51
2.52
414
C
2.53
2.54
S
2.55
2.56
2.57
2.58
2.59
2.6
2,61
0.4925
0.4927
0.4929
0:4929
04931
0.4931
0.4922
0.4932
WYDD
0.4934
04334
0.4936
1330
0.4938
ww330
0.4940
DOVENO
0.4941
0.4941
1.3
wypo
0.4943
0.4945
0.4946
0.4948
Varamu
0.4949
0.4951
0.4952
0.4953
0.4955
1.31
2.62
2.63
2.64
265
2.65
266
2.66
2.67
269
2.68
4:00
260
2.69
2.7
444
2.71
***
+ +-
2.72
2.73
6:23
2.74
Bar
2.75
2.76
2.77
2.78
2.79
בד ר
2.8
0.4956
0.4957
0.4959
0.4960
0.4961
01067
0.4962
01061
0.4963
0-1000
0.4964
...
0.4965
0-1300
0 1055
0.4966
0.7500
01067
0.4967
wywor
01040
0.4968
z
1.48
1.49
0.4969
0.000
0.4970
0.4971
0.4972
0.4973
0.4974
0.4974
1.5
1.51
1.52
1.53
1.54
1.55
1.56
1.57
1.58
1.59
1.6
1.61
1.62
1.63
1.64
1.65
1.66
A
0.4306
0.4319
0.4332
0.4345
0.4357
0.4370
0.4382
0.4394
0.4406
0.4418
0.4429
0.4441
0.4452
0.4463
0.4474
0.4484
0.4495
0.4505
0.4515
2.81
2.82
2.83
2.84
2.95
2.85
2.06
2.86
2.97
2.87
3.00
2.88
2.00
2.89
4:03
2.9
2.91
292
2.92
2.93
C
294
2.94
2.95
2.96
2.97
2.98
2.99
0.4975
0.4976
0.4977
04911
0.4977
0.4978
wkware
0.4979
Z
1.67
1.68
1.69
1.7
1.71
1.72
1.73
1.74
1.75
1.76
1.77
1.78
1.79
1.8
1.81
1.82
0.4979
0.4980
0.4981
wY00
0.4981
0.4981
0.4997
0.4982
0 4003
0.4982
0.4993
0.4983
0.4984
0.4984
0.4984
0.4985
0.4985
0.4986
0.4986
1.83
1.84
1.85
A
0.4525
0.4535
0.4545
0.4554
0.4564
0.4573
0.4582
0.4591
0.4599
0.4608
0.4616
0.4625
0.4633
0.4641
0.4649
0.4656
0.4664
0.4671
0.4678
3
3.01
3.02
3.03
3.04
3.05
3.06
3.00
3.07
3:07
1.00
3.08
3:00
3.09
3.1
11
3.11
3.12
3.13
3.14
3.15
3.16
3.17
3.18
0.4987
0.4987
0.4987
0.4988
0.4988
04020
0.4989
0.4989
0:4909
1000
0.4989
04990
0.4990
0.4990
4001
0.4990
0.4991
www
0.4991
0.4991
0.4992
0.4992
0.4992
0.4992
0.4993
Z
1.86
1.87
1.88
1.89
1.9
1.91
1.92
1.93
1.94
1.95
1.96
1.97
1.98
1.99
2
2.01
2.02
2.03
2.04
3.19
3.2
3.21
3.21
3.22
3.23
3:43
3.24
-
3.25
22
3.26
Se
3.27
1.30
3.28
3.29
Se
3.3
3.31
3.32
3.33
3.34
3.35
3.36
3.37
A
Z
0.4686 2.05
0.4693 2.06
0.4699 2.07
0.4706 2.08
0.4713 2.09
0.4719 2.1
0.4726 2.11
0.4732 2.12
0.4738 2.13
0.4744 2.14
0.4750 2.15
0.4756 2.16
0.4761 2.17
0.4767 2.18
0.4772 2.19
0.4778 2.2
0.4783 2.21
0.4788 2.22
0.4793 2.23
0.4993 3.38
0.4993 3.39
0.4993
3.4
0.4994
241
0.4994
9:32
6.1004
0.4994
3.41
242
3.42
2
3.43
3.44
****
34
04004
0.4994
W
04005
3.45
3:45
X
0.4995 3.46
3:10
0.4994
04005
0.4995
0.4995
0.4995
3.47
3.48
2.49
3:10
3:40
3.49
94329
0.4995 3.5
0.4995 3.51
0.4996 3.52
0.4996 3.53
0.4996
0.4996
0.4996
3.9
A
0.4798
0.4803
0.4808
0.4812
0.4817
0.4821
0.4826
0.4830
0.4834
0.4838
0.4842
0.4846
0.4850
0.4854
0.4857
0.4861
0.4864
0.4868
0.4871
0.4996
0.4997
0.4997
0.4997
0.4997
wwww
0.4007
0.4997
Bazz
04997
0.4997
Ba
0 4007
0.4997
04997
0.4997
S
0.4997
wwwww
0.4997
0.4998
wwwww
0.4998
0.4998
0.4998
0.4998
www
0.5000
Transcribed Image Text:Areas Under the Standard Normal Curve-The Values Were Generated Using the Standard Normal Distribution Function of Excel Note that the standard normal curve is symmetrical about the mean. z 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.11 0.12 Mean - 0 A 0.0000 0.0040 0.0080 0.0120 0.0160 0.0199 0.0239 0.0279 0.0319 0.0359 0.0398 0.0438 0.0478 z Z 0.13 0.14 0.15 0.16 0.17 0.18 0.19 0.2 0,21 0.22 0.23 0.24 0.25 A 0.0517 0.0557 0.0596 0.0636 0.0675 0.0714 0.0753 0.0793 0.0832 0.0871 0.0910 0.0948 0.0987 Z 0.26 0.27 0.28 0.29 0.3 0.31 0.32 0.33 0.34 0.35 0.36 0.37 0.38 A03413 2 = 1.00 A 0.1026 0.1064 0.1103 0.1141 0.1179 0.1217 0.1255 0.1293 0.1331 0.1368 0.1406 0.1443 0.1480 z 0.39 0.4 0.41 0.42 0.43 0.44 0.45 0.46 0.47 0.48 0.49 0.5 0.51 A 0.1517 0.1554 0.1591 0.1628 0.1664 0.1700 0.1736 0.1772 0.1808 0.1844 0.1879 0.1915 0.1950 z 0.52 0.53 0.54 0.55 0.56 0.57 0.58 0.59 0.6 0.61 0.62 0.63 0.64 A-0.4772 22.00 A 0.1985 0.2019 0.2054 0.2088 0.2123 0.2157 0.2190 0.2224 0.2257 0.2291 0.2324 0.2357 0.2389 z 0.65 0.66 0.67 0.68 0.69 0.7 0.71 0.72 0.73 0.74 0.75 0.76 0.77 A z 0.2422 0.78 0.2454 0.79 0.2486 0.2517 0.81 0.2549 0.82 0.2580 0.83 0.2611 0.84 0.2642 0.85 0.2673 0.86 0.2704 0.87 0.2734 0.88 0.2764 0.89 0.2794 0.9 A-0.4987 0.8 23.00 0.2823 0.2852 0.2881 0.2910 0.2939 0.2967 0.2995 0.3023 0.3051 0.3078 0.3106 0.3133 0.3159 Areas Under the Standard Normal Curve-The Values Were Generated Using the Standard Normal Distribution Function of Excel (continued) z 1.1 0.3186 0.3212 0.3238 1.11 0.3264 0.3289 0.3315 z 0.91 0.92 0.93 0.94 0.95 0.96 0.97 0.98 0.99 1 1.01 1.02 1.03 1.04 1.05 1.06 1.07 1.18 1.19 A z A 0.3643 1.29 0.4015 0.3665 0.4032 0.3686 0.4049 1.13 0.3708 1.32 0.4066 1.14 0.3729 1.33 0.4082 1.15 0.3749 1.34 0.4099 1.16 0.3770 1.35 0.4115 1.17 0.3790 1.36 0.4131 0.3810 1.37 0.4147 0.3830 1.38 0.4162 1.2 0.3849 1.39 0.4177 1.21 0.3869 1.4 0.4192 1.41 0.4207 1.22 0.3888 1.23 0.3907 1.42 0.4222 1.24 0.3925 1.43 0.4236 1.25 0.3944 1.44 0.4251 1.26 0.3962 1.45 0.4265 1.27 0.3980 1.46 0.4279 1.28 0.3997 1.47 0.4292 0.3340 0.3365 0.3389 0.3413 0.3438 0.3461 0.3485 0.3508 0.3531 0.3554 0.3577 0.3599 1.08 1.09 0.3621 2.28 ATAU in 20 2.29 22 2.3 and 444 2.31 And 444 2.32 444 2.33 2.34 B 2.25 2.35 4:DD 2.36 2.37 2.38 2.39 2.4 2.41 2.42 0.4878 0.4881 0:4001 O ARRA 0.4884 0.4887 0.Your 0 4900 0.4890 0.4893 0.1000 Areas Under the Standard Normal Curve-The Values Were Generated Using the Standard Normal Distribution Function of Excel (continued) 0.4875 2.43 2.24 2.25 2.26 2.44 2.45 222 2.27 2.46 247 2.47 0.1006 0.4896 0 4899 0.4898 0.1000 0.4001 0.4901 04904 0.4904 1.12 0.4906 0.7500 0.4909 0.4911 wayan 0.4913 0.4916 0.4918 0.4920 0.4922 2.48 2.49 26 2.5 3 2.51 2.52 414 C 2.53 2.54 S 2.55 2.56 2.57 2.58 2.59 2.6 2,61 0.4925 0.4927 0.4929 0:4929 04931 0.4931 0.4922 0.4932 WYDD 0.4934 04334 0.4936 1330 0.4938 ww330 0.4940 DOVENO 0.4941 0.4941 1.3 wypo 0.4943 0.4945 0.4946 0.4948 Varamu 0.4949 0.4951 0.4952 0.4953 0.4955 1.31 2.62 2.63 2.64 265 2.65 266 2.66 2.67 269 2.68 4:00 260 2.69 2.7 444 2.71 *** + +- 2.72 2.73 6:23 2.74 Bar 2.75 2.76 2.77 2.78 2.79 בד ר 2.8 0.4956 0.4957 0.4959 0.4960 0.4961 01067 0.4962 01061 0.4963 0-1000 0.4964 ... 0.4965 0-1300 0 1055 0.4966 0.7500 01067 0.4967 wywor 01040 0.4968 z 1.48 1.49 0.4969 0.000 0.4970 0.4971 0.4972 0.4973 0.4974 0.4974 1.5 1.51 1.52 1.53 1.54 1.55 1.56 1.57 1.58 1.59 1.6 1.61 1.62 1.63 1.64 1.65 1.66 A 0.4306 0.4319 0.4332 0.4345 0.4357 0.4370 0.4382 0.4394 0.4406 0.4418 0.4429 0.4441 0.4452 0.4463 0.4474 0.4484 0.4495 0.4505 0.4515 2.81 2.82 2.83 2.84 2.95 2.85 2.06 2.86 2.97 2.87 3.00 2.88 2.00 2.89 4:03 2.9 2.91 292 2.92 2.93 C 294 2.94 2.95 2.96 2.97 2.98 2.99 0.4975 0.4976 0.4977 04911 0.4977 0.4978 wkware 0.4979 Z 1.67 1.68 1.69 1.7 1.71 1.72 1.73 1.74 1.75 1.76 1.77 1.78 1.79 1.8 1.81 1.82 0.4979 0.4980 0.4981 wY00 0.4981 0.4981 0.4997 0.4982 0 4003 0.4982 0.4993 0.4983 0.4984 0.4984 0.4984 0.4985 0.4985 0.4986 0.4986 1.83 1.84 1.85 A 0.4525 0.4535 0.4545 0.4554 0.4564 0.4573 0.4582 0.4591 0.4599 0.4608 0.4616 0.4625 0.4633 0.4641 0.4649 0.4656 0.4664 0.4671 0.4678 3 3.01 3.02 3.03 3.04 3.05 3.06 3.00 3.07 3:07 1.00 3.08 3:00 3.09 3.1 11 3.11 3.12 3.13 3.14 3.15 3.16 3.17 3.18 0.4987 0.4987 0.4987 0.4988 0.4988 04020 0.4989 0.4989 0:4909 1000 0.4989 04990 0.4990 0.4990 4001 0.4990 0.4991 www 0.4991 0.4991 0.4992 0.4992 0.4992 0.4992 0.4993 Z 1.86 1.87 1.88 1.89 1.9 1.91 1.92 1.93 1.94 1.95 1.96 1.97 1.98 1.99 2 2.01 2.02 2.03 2.04 3.19 3.2 3.21 3.21 3.22 3.23 3:43 3.24 - 3.25 22 3.26 Se 3.27 1.30 3.28 3.29 Se 3.3 3.31 3.32 3.33 3.34 3.35 3.36 3.37 A Z 0.4686 2.05 0.4693 2.06 0.4699 2.07 0.4706 2.08 0.4713 2.09 0.4719 2.1 0.4726 2.11 0.4732 2.12 0.4738 2.13 0.4744 2.14 0.4750 2.15 0.4756 2.16 0.4761 2.17 0.4767 2.18 0.4772 2.19 0.4778 2.2 0.4783 2.21 0.4788 2.22 0.4793 2.23 0.4993 3.38 0.4993 3.39 0.4993 3.4 0.4994 241 0.4994 9:32 6.1004 0.4994 3.41 242 3.42 2 3.43 3.44 **** 34 04004 0.4994 W 04005 3.45 3:45 X 0.4995 3.46 3:10 0.4994 04005 0.4995 0.4995 0.4995 3.47 3.48 2.49 3:10 3:40 3.49 94329 0.4995 3.5 0.4995 3.51 0.4996 3.52 0.4996 3.53 0.4996 0.4996 0.4996 3.9 A 0.4798 0.4803 0.4808 0.4812 0.4817 0.4821 0.4826 0.4830 0.4834 0.4838 0.4842 0.4846 0.4850 0.4854 0.4857 0.4861 0.4864 0.4868 0.4871 0.4996 0.4997 0.4997 0.4997 0.4997 wwww 0.4007 0.4997 Bazz 04997 0.4997 Ba 0 4007 0.4997 04997 0.4997 S 0.4997 wwwww 0.4997 0.4998 wwwww 0.4998 0.4998 0.4998 0.4998 www 0.5000
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how do I find the probability that a bottle will be filled with more than 495 mililiters? I tried dividing the total frequencies from 495 up which was 102/122 and it gave me 0.8361 and it's saying it's wrong. I'm also getting that all my answers are wrong except for the first one which is 500 militers. 

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9780190698614
Author:
Sadiku, Matthew N. O.
Publisher:
Oxford University Press
Mechanics of Materials (10th Edition)
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:
9780134319650
Author:
Russell C. Hibbeler
Publisher:
PEARSON
Thermodynamics: An Engineering Approach
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:
9781259822674
Author:
Yunus A. Cengel Dr., Michael A. Boles
Publisher:
McGraw-Hill Education
Control Systems Engineering
Control Systems Engineering
Mechanical Engineering
ISBN:
9781118170519
Author:
Norman S. Nise
Publisher:
WILEY
Mechanics of Materials (MindTap Course List)
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:
9781337093347
Author:
Barry J. Goodno, James M. Gere
Publisher:
Cengage Learning
Engineering Mechanics: Statics
Engineering Mechanics: Statics
Mechanical Engineering
ISBN:
9781118807330
Author:
James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher:
WILEY