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 £?

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Answer 3 and 4 and 5 with graphs

TABLE D.1
AREAS UNDER THE STANDARDIZED NORMAL DISTRIBUTION
Example
Pr (0sZs1.96) = 0.4750
Pr(Z 21.96) = 0.5 - 0.4750 = 0.025
0.4750
X - u
Z =
1.96
.00
.01
.02
.03
.04
.05
.06
.07
.08
.09
.0000
.0398
.0040
.0080
.0319
0.0
0.1
.0120
.0160
.0199
.0239
.0279
.0359
.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
.1664
.1331
.1700
.1368
.1406
.1772
.1443
.1480
.1517
0.4
0.5
.1879
2224
.1554
.1591
.1628
.1736
.1808
.1844
.1915
.1950
.1985
.2019
.2054
.2088
2123
.2157
2190
2257
2580
0.6
2291
.2324
2357
2389
.2422
2454
2486
2517
.2549
0.7
.2611
.2642
.2673
.2704
.2734
2764
.2794
2823
2852
0.8
.2881
.2910
.2939
.2967
2995
3023
.3051
.3078
.3106
.3133
.3159
.3315
0.9
1.0
.3186
.3212
.3461
.3238
.3485
.3264
.3508
.3289
.3531
.3340
.3577
.3365
.3599
.3389
.3621
.3413
.3438
.3554
.3708
.3907
1.1
.3643
.3830
.3665
.3869
.3686
.3729
.3749
.3770
.3790
.3810
1.2
.3849
.3888
.3925
.3944
.3962
.3980
3997
4015
1.3
4032
.4049
.4066
.4082
.4099
.4115
.4131
.4147
.4162
.4177
4279
1.4
1.5
.4192
.4207
.4222
.4236
.4251
.4265
4292
4306
.4319
4332
.4345
.4357
.4370
.4382
.4394
4406
.4418
4429
.4441
.4495
.4515
4535
.4625
1.6
.4452
.4454
.4463
.4564
.4474
.4573
.4484
.4582
.4505
.4525
.4616
.4545
.4633
1.7
.4591
.4599
.4608
1.8
.4641
.4649
.4656
.4664
.4671
.4678
.4686
.4693
4756
4699
.4706
1.9
.4713
.4719
.4726
.4732
.4738
.4744
.4750
.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
.4868
.4871
.4901
.4878
.4906
.4881
.4887
4913
4890
.4916
2.2
.4861
.4893
.4864
.4875
4884
2.3
.4896
.4898
.4904
.4909
.4911
2.4
2.5
.4918
4938
.4920
.4922
.4941
.4925
.4927
.4945
.4929
.4946
.4931
4948
.4932
.4949
.4934
.4951
4936
.4952
.4940
.4943
4961
.4964
2.6
2.7
.4953
.4965
.4955
.4966
.4956
.4957
.4959
.4960
.4962
.4963
.4967
.4968
.4969
.4970
.4971
4972
4973
4974
2.8
.4974
.4975
.4976
.4977
.4977
.4978
4979
.4979
4980 .4981
2.9
3.0
.4981
.4987
.4982
.4987
4982
.4983
.4984
.4984
.4985
4985
4986
.4986
.4987
.4988
.4988
.4989
.4989
.4989
4990
4990
Note: This table gives the area in the right-hand tail of the distribution (i.e., Zz 0). But since the normal
distribution is symmetrical about 2=0, the area in the left-hand tail is the same as the area in the corrosponding
right-hand tail. For example, P(-1.96 s Z<0) = 0.4750. Thorofore, P-1.96 sZs 1.96) = 2(0.4750) = 0.95.
6789 o
O O O 000
2222N2
222 N3
Transcribed Image Text:TABLE D.1 AREAS UNDER THE STANDARDIZED NORMAL DISTRIBUTION Example Pr (0sZs1.96) = 0.4750 Pr(Z 21.96) = 0.5 - 0.4750 = 0.025 0.4750 X - u Z = 1.96 .00 .01 .02 .03 .04 .05 .06 .07 .08 .09 .0000 .0398 .0040 .0080 .0319 0.0 0.1 .0120 .0160 .0199 .0239 .0279 .0359 .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 .1664 .1331 .1700 .1368 .1406 .1772 .1443 .1480 .1517 0.4 0.5 .1879 2224 .1554 .1591 .1628 .1736 .1808 .1844 .1915 .1950 .1985 .2019 .2054 .2088 2123 .2157 2190 2257 2580 0.6 2291 .2324 2357 2389 .2422 2454 2486 2517 .2549 0.7 .2611 .2642 .2673 .2704 .2734 2764 .2794 2823 2852 0.8 .2881 .2910 .2939 .2967 2995 3023 .3051 .3078 .3106 .3133 .3159 .3315 0.9 1.0 .3186 .3212 .3461 .3238 .3485 .3264 .3508 .3289 .3531 .3340 .3577 .3365 .3599 .3389 .3621 .3413 .3438 .3554 .3708 .3907 1.1 .3643 .3830 .3665 .3869 .3686 .3729 .3749 .3770 .3790 .3810 1.2 .3849 .3888 .3925 .3944 .3962 .3980 3997 4015 1.3 4032 .4049 .4066 .4082 .4099 .4115 .4131 .4147 .4162 .4177 4279 1.4 1.5 .4192 .4207 .4222 .4236 .4251 .4265 4292 4306 .4319 4332 .4345 .4357 .4370 .4382 .4394 4406 .4418 4429 .4441 .4495 .4515 4535 .4625 1.6 .4452 .4454 .4463 .4564 .4474 .4573 .4484 .4582 .4505 .4525 .4616 .4545 .4633 1.7 .4591 .4599 .4608 1.8 .4641 .4649 .4656 .4664 .4671 .4678 .4686 .4693 4756 4699 .4706 1.9 .4713 .4719 .4726 .4732 .4738 .4744 .4750 .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 .4868 .4871 .4901 .4878 .4906 .4881 .4887 4913 4890 .4916 2.2 .4861 .4893 .4864 .4875 4884 2.3 .4896 .4898 .4904 .4909 .4911 2.4 2.5 .4918 4938 .4920 .4922 .4941 .4925 .4927 .4945 .4929 .4946 .4931 4948 .4932 .4949 .4934 .4951 4936 .4952 .4940 .4943 4961 .4964 2.6 2.7 .4953 .4965 .4955 .4966 .4956 .4957 .4959 .4960 .4962 .4963 .4967 .4968 .4969 .4970 .4971 4972 4973 4974 2.8 .4974 .4975 .4976 .4977 .4977 .4978 4979 .4979 4980 .4981 2.9 3.0 .4981 .4987 .4982 .4987 4982 .4983 .4984 .4984 .4985 4985 4986 .4986 .4987 .4988 .4988 .4989 .4989 .4989 4990 4990 Note: This table gives the area in the right-hand tail of the distribution (i.e., Zz 0). But since the normal distribution is symmetrical about 2=0, the area in the left-hand tail is the same as the area in the corrosponding right-hand tail. For example, P(-1.96 s Z<0) = 0.4750. Thorofore, P-1.96 sZs 1.96) = 2(0.4750) = 0.95. 6789 o O O O 000 2222N2 222 N3
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 £?
Transcribed Image Text: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 £?
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