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(a) Sam and Peter are classmates. In an examination, Sam gets 75 marks and Peter gets 89 marks. It is known that the standard normal score of Sam's marks is 0, zSam) = 0 and the standard normal score of %3! Peter's marks is 1.75, z Peter) = 1.75. Find the standard deviation of the examination marks.

(a) Sam and Peter are classmates. In an examination, Sam gets 75 marks and Peter gets 89 marks. It is known that the standard normal score of Sam's marks is 0, zSam) = 0 and the standard normal score of %3! Peter's marks is 1.75, z Peter) = 1.75. Find the standard deviation of the examination marks.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 22PFA
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Elementary Statistics Question 6 (For question 6, just write down the answer. No explanation is needed.) (a) Sam and Peter are classmates. In an examination, Sam gets 75 marks and Peter gets 89 marks. It is known that the standard normal score of Sam's marks is 0, zSam) = 0 and the standard normal score of Peter's marks is 1.75, z(Peter) = 1.75. Find the standard deviation of the examination marks. (b) The table below indicates the number of refund cases and the average amount of refund per case in January to March by a department store: January February March Number of refund cases 12 12 6 received in a month Average amount of refund $660 $780 $1000 per case in a month Find the overall average amount of refund per case between January and March. (c) In a city, the consumer price index in 2015, 2016, and 2017 were 100, 108.5, and 113.5 respectively. Find the percentage change of price from 2016 to 2017. (d) Write down the name of the sampling method for the following cases: (di) A fair representative of staff members is selected randomly from different education levels to conduct a survey on the relationship between promotion prospects and education level. (dii) The first student of every 10 students who leave a lecture hall is asked to comment on the teaching effectiveness of the lesson.
Transcribed Image Text:Elementary Statistics Question 6 (For question 6, just write down the answer. No explanation is needed.) (a) Sam and Peter are classmates. In an examination, Sam gets 75 marks and Peter gets 89 marks. It is known that the standard normal score of Sam's marks is 0, zSam) = 0 and the standard normal score of Peter's marks is 1.75, z(Peter) = 1.75. Find the standard deviation of the examination marks. (b) The table below indicates the number of refund cases and the average amount of refund per case in January to March by a department store: January February March Number of refund cases 12 12 6 received in a month Average amount of refund $660 $780 $1000 per case in a month Find the overall average amount of refund per case between January and March. (c) In a city, the consumer price index in 2015, 2016, and 2017 were 100, 108.5, and 113.5 respectively. Find the percentage change of price from 2016 to 2017. (d) Write down the name of the sampling method for the following cases: (di) A fair representative of staff members is selected randomly from different education levels to conduct a survey on the relationship between promotion prospects and education level. (dii) The first student of every 10 students who leave a lecture hall is asked to comment on the teaching effectiveness of the lesson.
Elementary Starities The entries in Table I are the probabilities that a random variable having the standard normal distribution will take on a value between 0 and . They are given by the area of the gray region under the curve in the figure. TABLE I NORMAL-CURVE AREAS 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 0.1985 0.1664 0.1700 0.1736 0.1772 0.1808 0.1844 0.1879 0.5 0.1915 0.1950 0.2019 0.2054 0.2088 0.2123 0.2157 0.2190 0.2224 0.6 0.2257 0.2357 0.2517 0.2549 0.2291 0.2611 0.2324 0.2389 0.2422 0.2734 0.2454 0.2486 0.7 0.2580 0.2642 0.2704 0.2764 0.2794 0.2823 0.2852 0.2673 0.2967 0.2939 0.3023 0.3051 0.3106 0.2995 0.3264 0.8 0.2881 0.2910 0.3078 0.3133 0.9 0.3340 0.3186 0.3438 0.9 0.3159 0.3212 0.3238 0.3289 0.3315 0.3365 0.3389 1.0 0.3413 0.3461 0.3485 0.3508 0.3531 0.3554 0.3577 0.3599 0.3621 0.3729 0.3925 0.3830 0.4015 0.4177 0.3643 0.3665 0.3686 0.3708 0.3749 0.3770 0.3790 0.3810 1.2 1.3 0.3849 0.3869 0.3888 0.3907 0.3944 0.3962 0.3980 0.3997 0.4032 0.4049 0.4066 0.4082 0.4099 0.4115 0.4131 0.4147 0.4162 0.4319 0.4192 0.4332 1.4 0.4207 0.4222 0.4236 0.4251 0,4265 0.4279 0.4292 0.4306 1.5 0.4345 0,4357 0.4370 0.4382 0.4394 0.4406 0.4418 0.4429 0.4441 0.4525 0.4452 0.4554 1.6 0.4463 0.4474 0.4484 0.4495 0.4505 0.4515 0.4535 0.4545 0.4616 0.4692 1.7 0.4564 0.4573 0.4582 0.4591 0.4599 0.4608 0.4625 0.4633 1.8 0.4641 0.4648 0.4656 0.4664 0.4671 0.4678 0.4685 0.4699 0.4706 0.4744 0.4756 0.4808 0.4732 0.4738 0.4750 0.4761 0.4767 0.4713 0.4772 1.9 0.4719 0.4725 2.0 0.4778 0.4783 0.4788 0.4793 0.4798 0.4803 0.4812 0.4817 0.4857 0.4826 0.4864 0.4830 0.4868 2.1 0.4821 0.4834 0.4838 0.4842 0.4846 0.4850 0.4854 2.2 0.4861 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 0.4925 0.4943 2.4 0.4918 0.4920 0.4922 0.4927 0.4929 0.4931 0.4932 0.4934 0.4936 2.5 0.4938 0.4940 0.4941 0.4945 0.4946 0.4948 0.4949 0.4951 0.4952 0.4962 0.4972 0.4979 2.6 0.4953 0.4955 0.4956 0.4957 0.4959 0.4960 0.4961 0.4963 0.4964 2.7 0.4965 0.4966 0.4967 0.4968 0.4969 0.4970 0.4971 0.4973 0.4974 0.4980 0.4986 0.4990 0.4981 0.4977 0.4983 2.8 0.4974 0.4975 0.4976 0.4977 0.4978 0.4979 2.9 0.4981 0.4982 0.4982 0.4984 0.4984 0.4985 0.4985 0.4986 3.0 0.4987 0.4987 0.4987 0.4988 0.4988 0.4989 0.4989 0.4989 0.4990 Also, for z- 4.0, 5.0 and 6.0, the areas are 0.49997, 0.4999997, and 0.499999999.
Transcribed Image Text:Elementary Starities The entries in Table I are the probabilities that a random variable having the standard normal distribution will take on a value between 0 and . They are given by the area of the gray region under the curve in the figure. TABLE I NORMAL-CURVE AREAS 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 0.1985 0.1664 0.1700 0.1736 0.1772 0.1808 0.1844 0.1879 0.5 0.1915 0.1950 0.2019 0.2054 0.2088 0.2123 0.2157 0.2190 0.2224 0.6 0.2257 0.2357 0.2517 0.2549 0.2291 0.2611 0.2324 0.2389 0.2422 0.2734 0.2454 0.2486 0.7 0.2580 0.2642 0.2704 0.2764 0.2794 0.2823 0.2852 0.2673 0.2967 0.2939 0.3023 0.3051 0.3106 0.2995 0.3264 0.8 0.2881 0.2910 0.3078 0.3133 0.9 0.3340 0.3186 0.3438 0.9 0.3159 0.3212 0.3238 0.3289 0.3315 0.3365 0.3389 1.0 0.3413 0.3461 0.3485 0.3508 0.3531 0.3554 0.3577 0.3599 0.3621 0.3729 0.3925 0.3830 0.4015 0.4177 0.3643 0.3665 0.3686 0.3708 0.3749 0.3770 0.3790 0.3810 1.2 1.3 0.3849 0.3869 0.3888 0.3907 0.3944 0.3962 0.3980 0.3997 0.4032 0.4049 0.4066 0.4082 0.4099 0.4115 0.4131 0.4147 0.4162 0.4319 0.4192 0.4332 1.4 0.4207 0.4222 0.4236 0.4251 0,4265 0.4279 0.4292 0.4306 1.5 0.4345 0,4357 0.4370 0.4382 0.4394 0.4406 0.4418 0.4429 0.4441 0.4525 0.4452 0.4554 1.6 0.4463 0.4474 0.4484 0.4495 0.4505 0.4515 0.4535 0.4545 0.4616 0.4692 1.7 0.4564 0.4573 0.4582 0.4591 0.4599 0.4608 0.4625 0.4633 1.8 0.4641 0.4648 0.4656 0.4664 0.4671 0.4678 0.4685 0.4699 0.4706 0.4744 0.4756 0.4808 0.4732 0.4738 0.4750 0.4761 0.4767 0.4713 0.4772 1.9 0.4719 0.4725 2.0 0.4778 0.4783 0.4788 0.4793 0.4798 0.4803 0.4812 0.4817 0.4857 0.4826 0.4864 0.4830 0.4868 2.1 0.4821 0.4834 0.4838 0.4842 0.4846 0.4850 0.4854 2.2 0.4861 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 0.4925 0.4943 2.4 0.4918 0.4920 0.4922 0.4927 0.4929 0.4931 0.4932 0.4934 0.4936 2.5 0.4938 0.4940 0.4941 0.4945 0.4946 0.4948 0.4949 0.4951 0.4952 0.4962 0.4972 0.4979 2.6 0.4953 0.4955 0.4956 0.4957 0.4959 0.4960 0.4961 0.4963 0.4964 2.7 0.4965 0.4966 0.4967 0.4968 0.4969 0.4970 0.4971 0.4973 0.4974 0.4980 0.4986 0.4990 0.4981 0.4977 0.4983 2.8 0.4974 0.4975 0.4976 0.4977 0.4978 0.4979 2.9 0.4981 0.4982 0.4982 0.4984 0.4984 0.4985 0.4985 0.4986 3.0 0.4987 0.4987 0.4987 0.4988 0.4988 0.4989 0.4989 0.4989 0.4990 Also, for z- 4.0, 5.0 and 6.0, the areas are 0.49997, 0.4999997, and 0.499999999.
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