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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 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=

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
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
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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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