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The management of a supermarket wants to adopt a new promotional policy of giving free gift to every customer who spends more than a certain amount per visit at this supermarket. The expectation of the management is that after this promotional policy is advertised, the expenditure for all customers at this supermarket will be normally distributed with mean 400 £ and a variance of 900 £?. 1) If the management wants to give free gifts to at most 10% of the customers, what should the amount be above which a customer would receive a free gift? 2) In a sample of 100 customers, what are the number of customers whose expenditure is between 420 £ and 485 £? 3) What is a probability of selecting a customer whose expenditure is differ than the population mean expenditure by at most 50 £?

The management of a supermarket wants to adopt a new promotional policy of giving free gift to every customer who spends more than a certain amount per visit at this supermarket. The expectation of the management is that after this promotional policy is advertised, the expenditure for all customers at this supermarket will be normally distributed with mean 400 £ and a variance of 900 £?. 1) If the management wants to give free gifts to at most 10% of the customers, what should the amount be above which a customer would receive a free gift? 2) In a sample of 100 customers, what are the number of customers whose expenditure is between 420 £ and 485 £? 3) What is a probability of selecting a customer whose expenditure is differ than the population mean expenditure by at most 50 £?

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
Section: Chapter Questions
Problem 22SGR
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4G 435 12:54 PM 80 B/s Mar 20, 2021 PM 12:17 TABLE D.1 AREAS UNDER THE STANDARDIZED NORMAL DISTRIBUTION Example Pr (0<Z<1.96) = 0.4750 Pr(Z>1.96) = 0.5 – 0.4750 = 0.025 0.4750 1.96 .00 .01 .02 .03 .04 .05 .06 .07 .08 .09 0.0 .0000 .0040 .0080 .0120 .0160 .0199 .0239 .0279 .0319 .0359 0.1 .0398 .0438 .0478 .0517 .0557 .0596 .0636 .0675 .0714 .0753 0.2 .0793 .0832 .0871 .0910 .0948 .0987 .1026 .1064 .1103 .1141 0.3 .1179 .1217 .1255 .1293 .1331 .1368 .1406 .1443 .1480 .1517 0.4 .1554 .1591 .1628 .1664 .1700 .1736 .1772 .1808 .1844 .1879 0.5 .1915 .1950 .1985 .2019 .2054 .2088 .2123 .2157 .2190 .2224 .2454 .2764 0.6 .2257 .2291 .2324 .2357 .2389 .2422 .2486 .2517 .2549 .2580 .2881 0.7 .2611 .2642 .2673 .2704 .2734 .2794 .2823 .2852 .2939 .3212 .3461 0.8 .2910 .2967 .2995 .3023 .3051 .3078 .3106 .3133 .3389 .3621 0.9 .3159 .3186 .3238 .3264 .3289 .3315 .3340 .3365 1.0 .3413 .3438 .3485 .3508 .3531 .3554 .3577 .3599 1.1 .3643 .3665 .3686 .3708 .3729 .3749 .3770 .3790 .3810 .3830 1.2 .3849 .3869 .3888 .3907 .3925 .3944 .3962 .3980 .3997 .4015 1.3 .4032 .4049 .4066 .4082 4099 .4115 .4131 .4147 .4162 .4177 1.4 .4192 .4207 .4222 .4236 .4251 .4265 .4279 .4292 .4306 .4319 1.5 .4332 .4345 .4357 .4370 .4382 .4394 .4406 .4418 .4429 .4441 .4505 .4599 .4678 .4744 1.6 .4452 .4463 .4474 .4484 .4495 .4515 .4525 .4535 .4545 .4582 .4664 .4591 .4671 .4738 1.7 .4454 .4564 .4573 .4608 .4616 .4625 .4633 1.8 .4641 .4649 .4656 .4686 .4693 .4699 .4706 1.9 .4713 .4719 .4726 .4732 .4750 .4756 .4761 .4767 2.0 .4772 .4778 .4783 .4788 .4793 .4798 .4803 .4808 .4812 .4817 2.1 .4821 .4826 .4830 .4834 .4838 .4842 .4846 .4850 .4854 .4857 2.2 .4861 .4864 .4868 .4871 .4875 .4878 .4881 .4884 .4887 .4890 .4904 .4913 .4934 2.3 .4893 .4896 .4898 .4901 .4906 .4909 .4911 .4916 .4922 .4927 .4932 .4931 .4948 2.4 .4918 .4920 .4925 .4929 .4936 2.5 .4938 .4940 .4941 .4943 .4945 .4946 .4949 .4951 .4952 2.6 .4953 .4955 .4956 .4957 .4959 .4960 .4961 .4962 .4963 .4964 2.7 .4965 .4966 .4967 .4968 .4969 .4970 .4971 .4972 .4973 .4974 .4975 .4976 4977 .4978 .4979 .4980 4981 2.9 .4981 .4982 .4982 .4983 .4984 .4984 .4985 .4985 .4986 .4986 3.0 .4987 .4987 .4987 .4988 .4988 .4989 .4989 .4989 .4990 .4990 Note: This table gives the area in the right-hand tail of the distribution (i.e., Z > 0). But since the normal distribution is symmetrical about Z= 0, the area in the left-hand tail is the same as the area in the corresponding right-hand tail. For example, P(–1.96 < Z< 0) = 0.4750. Therefore, P(-1.96 < Z< 1.96) = 2(0.4750) = 0.95. Share Edit Delete More ON 0 o O O O O OO
Transcribed Image Text:4G 435 12:54 PM 80 B/s Mar 20, 2021 PM 12:17 TABLE D.1 AREAS UNDER THE STANDARDIZED NORMAL DISTRIBUTION Example Pr (0<Z<1.96) = 0.4750 Pr(Z>1.96) = 0.5 – 0.4750 = 0.025 0.4750 1.96 .00 .01 .02 .03 .04 .05 .06 .07 .08 .09 0.0 .0000 .0040 .0080 .0120 .0160 .0199 .0239 .0279 .0319 .0359 0.1 .0398 .0438 .0478 .0517 .0557 .0596 .0636 .0675 .0714 .0753 0.2 .0793 .0832 .0871 .0910 .0948 .0987 .1026 .1064 .1103 .1141 0.3 .1179 .1217 .1255 .1293 .1331 .1368 .1406 .1443 .1480 .1517 0.4 .1554 .1591 .1628 .1664 .1700 .1736 .1772 .1808 .1844 .1879 0.5 .1915 .1950 .1985 .2019 .2054 .2088 .2123 .2157 .2190 .2224 .2454 .2764 0.6 .2257 .2291 .2324 .2357 .2389 .2422 .2486 .2517 .2549 .2580 .2881 0.7 .2611 .2642 .2673 .2704 .2734 .2794 .2823 .2852 .2939 .3212 .3461 0.8 .2910 .2967 .2995 .3023 .3051 .3078 .3106 .3133 .3389 .3621 0.9 .3159 .3186 .3238 .3264 .3289 .3315 .3340 .3365 1.0 .3413 .3438 .3485 .3508 .3531 .3554 .3577 .3599 1.1 .3643 .3665 .3686 .3708 .3729 .3749 .3770 .3790 .3810 .3830 1.2 .3849 .3869 .3888 .3907 .3925 .3944 .3962 .3980 .3997 .4015 1.3 .4032 .4049 .4066 .4082 4099 .4115 .4131 .4147 .4162 .4177 1.4 .4192 .4207 .4222 .4236 .4251 .4265 .4279 .4292 .4306 .4319 1.5 .4332 .4345 .4357 .4370 .4382 .4394 .4406 .4418 .4429 .4441 .4505 .4599 .4678 .4744 1.6 .4452 .4463 .4474 .4484 .4495 .4515 .4525 .4535 .4545 .4582 .4664 .4591 .4671 .4738 1.7 .4454 .4564 .4573 .4608 .4616 .4625 .4633 1.8 .4641 .4649 .4656 .4686 .4693 .4699 .4706 1.9 .4713 .4719 .4726 .4732 .4750 .4756 .4761 .4767 2.0 .4772 .4778 .4783 .4788 .4793 .4798 .4803 .4808 .4812 .4817 2.1 .4821 .4826 .4830 .4834 .4838 .4842 .4846 .4850 .4854 .4857 2.2 .4861 .4864 .4868 .4871 .4875 .4878 .4881 .4884 .4887 .4890 .4904 .4913 .4934 2.3 .4893 .4896 .4898 .4901 .4906 .4909 .4911 .4916 .4922 .4927 .4932 .4931 .4948 2.4 .4918 .4920 .4925 .4929 .4936 2.5 .4938 .4940 .4941 .4943 .4945 .4946 .4949 .4951 .4952 2.6 .4953 .4955 .4956 .4957 .4959 .4960 .4961 .4962 .4963 .4964 2.7 .4965 .4966 .4967 .4968 .4969 .4970 .4971 .4972 .4973 .4974 .4975 .4976 4977 .4978 .4979 .4980 4981 2.9 .4981 .4982 .4982 .4983 .4984 .4984 .4985 .4985 .4986 .4986 3.0 .4987 .4987 .4987 .4988 .4988 .4989 .4989 .4989 .4990 .4990 Note: This table gives the area in the right-hand tail of the distribution (i.e., Z > 0). But since the normal distribution is symmetrical about Z= 0, the area in the left-hand tail is the same as the area in the corresponding right-hand tail. For example, P(–1.96 < Z< 0) = 0.4750. Therefore, P(-1.96 < Z< 1.96) = 2(0.4750) = 0.95. Share Edit Delete More ON 0 o O O O O OO
4G 486 12:55 PM • 80 B/s Mar 20, 2021 PM 12:13 Question Five The management of a supermarket wants to adopt a new promotional policy of giving free gift to every customer who spends more than a certain amount per visit at this supermarket. The expectation of the management is that after this promotional policy is advertised, the expenditure for all customers at this supermarket will be normally distributed with mean 400 £ and a variance of 900 £?. 1) If the management wants to give free gifts to at most 10% of the customers, what should the amount be above which a customer would receive a free gift? 2) In a sample of 100 customers, what are the number of customers whose expenditure is between 420 £ and 485 £? 3) What is a probability of selecting a customer whose expenditure is differ than the population mean expenditure by at most 50 £? 4) In a sample of 49 customers, what are the number of customers whose mean expenditure is at least 410 £? 5) What is the probability that the expenditure of the first customer exceeds the expenditure of the second customer by at least 20 £? Share Edit Delete More
Transcribed Image Text:4G 486 12:55 PM • 80 B/s Mar 20, 2021 PM 12:13 Question Five The management of a supermarket wants to adopt a new promotional policy of giving free gift to every customer who spends more than a certain amount per visit at this supermarket. The expectation of the management is that after this promotional policy is advertised, the expenditure for all customers at this supermarket will be normally distributed with mean 400 £ and a variance of 900 £?. 1) If the management wants to give free gifts to at most 10% of the customers, what should the amount be above which a customer would receive a free gift? 2) In a sample of 100 customers, what are the number of customers whose expenditure is between 420 £ and 485 £? 3) What is a probability of selecting a customer whose expenditure is differ than the population mean expenditure by at most 50 £? 4) In a sample of 49 customers, what are the number of customers whose mean expenditure is at least 410 £? 5) What is the probability that the expenditure of the first customer exceeds the expenditure of the second customer by at least 20 £? Share Edit Delete More
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