GSN403 The Standard Normal Distribution Table Normal Curve Areas z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.0 0.0000 0.0040 0.0080 0.0120 0.0160 0.0199 0.0239 0.0279 0.0319 0.0359 0.1...

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Soda Water

A soft drink factory fills cans of soda water by setting a timer on a filling machine. It has been found that the distribution of the amount of soda water the machine puts into a can is normal with standard deviation of 1 ml.




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The Standard Normal Distribution Table Probability given in table represents P(0






GSN403 The Standard Normal Distribution Table Normal Curve Areas z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.0 0.0000 0.0040 0.0080 0.0120 0.0160 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 0.0910 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 0.1480 0.1517 0.4 0.1554 0.1591 0.1628 0.1664 0.1700 0.1736 0.1772 0.1808 0.1844 0.1879 0.5 0.1915 0.1950 0.1985 0.2019 0.2054 0.2088 0.2123 0.2157 0.2190 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 0.2580 0.2611 0.2642 0.2673 0.2704 0.2734 0.2764 0.2794 0.2823 0.2852 0.8 0.2881 0.2910 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 0.3340 0.3365 0.3389 1.0 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 0.3770 0.3790 0.3810 0.3830 1.2 0.3849 0.3869 0.3888 0.3907 0.3925 0.3944 0.3962 0.3980 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 0.4370 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 0.4591 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 0.4750 0.4756 0.4761 0.4767 2.0 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 0.4830 0.4834 0.4838 0.4842 0.4846 0.4850 0.4854 0.4857 2.2 0.4861 0.4864 0.4868 0.4871 0.4875 0.4878 0.4881 0.4884 0.4887 0.4890 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 0.4920 0.4922 0.4925 0.4927 0.4929 0.4931 0.4932 0.4934 0.4936 2.5 0.4938 0.4940 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 0.4960 0.4961 0.4962 0.4963 0.4964 2.7 0.4965 0.4966 0.4967 0.4968 0.4969 0.4970 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 0.4980 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 0.4987 0.4987 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 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 3.5 0.4998 0.4998 0.4998 0.4998 0.4998 0.4998 0.4998 0.4998 0.4998 0.4998 The Inverse Normal Table Given a probability in the tail this table gives the corresponding z score Area in Right Hand Tail = a a z score a z score a z score 0.5 0.0000 0.3 0.5244 0.1 1.2816 0.49 0.0251 0.29 0.5534 0.09 1.3408 0.48 0.0502 0.28 0.5828 0.08 1.4051 0.47 0.0753 0.27 0.6128 0.07 1.4758 0.46 0.1004 0.26 0.6433 0.06 1.5548 0.45 0.1257 0.25 0.6745 0.05 1.6449 0.44 0.1510 0.24 0.7063 0.04 1.7507 0.43 0.1764 0.23 0.7388 0.03 1.8808 0.42 0.2019 0.22 0.7722 0.025 1.9600 0.41 0.2275 0.21 0.8064 0.02 2.0537 0.4 0.2533 0.2 0.8416 0.01 2.3263 0.39 0.2793 0.19 0.8779 0.009 2.3656 0.38 0.3055 0.18 0.9154 0.008 2.4089 0.37 0.3319 0.17 0.9542 0.007 2.4573 0.36 0.3585 0.16 0.9945 0.006 2.5121 0.35 0.3853 0.15 1.0364 0.005 2.5758 0.34 0.4125 0.14 1.0803 0.004 2.6521 0.33 0.4399 0.13 1.1264 0.003 2.7478 0.32 0.4677 0.12 1.1750 0.002 2.8782 0.31 0.4958 0.11 1.2265 0.001 3.0902 a - area in right hand tail 0 z Probability given in table represents P(0 <>< z). tutorial details continuous probability distributions soda water a soft drink factory fills cans of soda water by setting a timer on a filling machine. it has been found that the distribution of the amount of soda water the machine puts into a can is normal with standard deviation of 1 ml. (a) if the company wants 99.9% of all its cans of soda water to have at least 375 ml as printed on the container, what mean amount should the filling machine be set to put in each can? (4 marks) (b)using the mean obtained in part (a), find out (use standard normal table) (i) the range of the middle 70% of cans. (ii)the minimum volume of the top 2% of cans. (6 marks) you must draw graphs for each question and show all workings. answers without clearly labelled graphs and full workings will not score full marks. submission instructions: 1. submit your tha as a single document in pdf format 1 z).="" tutorial="" details="" continuous="" probability="" distributions="" soda="" water="" a="" soft="" drink="" factory="" fills="" cans="" of="" soda="" water="" by="" setting="" a="" timer="" on="" a="" filling="" machine.="" it="" has="" been="" found="" that="" the="" distribution="" of="" the="" amount="" of="" soda="" water="" the="" machine="" puts="" into="" a="" can="" is="" normal="" with="" standard="" deviation="" of="" 1="" ml.="" (a)="" if="" the="" company="" wants="" 99.9%="" of="" all="" its="" cans="" of="" soda="" water="" to="" have="" at="" least="" 375="" ml="" as="" printed="" on="" the="" container,="" what="" mean="" amount="" should="" the="" filling="" machine="" be="" set="" to="" put="" in="" each="" can?="" (4="" marks)="" (b)="" using="" the="" mean="" obtained="" in="" part="" (a),="" find="" out="" (use="" standard="" normal="" table)="" (i)="" the="" range="" of="" the="" middle="" 70%="" of="" cans.="" (ii)="" the="" minimum="" volume="" of="" the="" top="" 2%="" of="" cans.="" (6="" marks)="" you="" must="" draw="" graphs="" for="" each="" question="" and="" show="" all="" workings.="" answers="" without="" clearly="" labelled="" graphs="" and="" full="" workings="" will="" not="" score="" full="" marks.="" submission="" instructions:="" 1.="" submit="" your="" tha="" as="" a="" single="" document="" in="" pdf="" format="">
Answered Same DayDec 27, 2021

Answer To: GSN403 The Standard Normal Distribution Table Normal Curve Areas z 0.00 0.01 0.02 0.03 0.04 0.05...

David answered on Dec 27 2021
114 Votes
TUTORIAL DETAILS
1
Continuous Probability Distributions
Soda Water
A soft drink factory fills
cans of soda water by setting a timer on a filling machine. It has
been found that the distribution of the amount of soda water the machine puts into a can is
normal with standard deviation of 1 ml.
(a) If the company wants 99.9% of all its cans of soda water to have at least 375 ml as
printed on the container, what mean amount should the filling machine be set to put
in each can?
(4 marks)
Let the mean amount is ml. Given,
P(X > 375) = 0.999
(


)
From standard normal table,...
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