Question FiveThe management of a supermarket wants to adopt a new promotional policy ofgiving free gift to every customer who spends more than a certain amount per visitat this supermarket. The expectation of the management is that after thispromotional policy is advertised, the expenditure for all customers at thissupermarket 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 freegift?2) In a sample of 100 customers, what are the number of customers whoseexpenditure is between 420 £ and 485 £?3) What is a probability of selecting a customer whose expenditure is differ thanthe population mean expenditure by at most 50 £?4) In a sample of 49 customers, what are the number of customers whosemean expenditure is at least 410 £?5) What is the probability that the expenditure of the first customer exceeds theexpenditure of the second customer by at least 20 £? TABLE D.1AREAS UNDER THE STANDARDIZED NORMAL DISTRIBUTIONExamplePr(0sZ 1.96) -0.4750Pr(Z21.96) -0.5 - 0.4750 -0.0250.47501.96.00.01.02.03.04.05.06.07.08.09.0359.07530160.0279.0319.0714.1103.1480.0080.0120.0517.0199.0596.02390.010.1.0000.0398.0793.1179.0040.0636.1026.0438.0478.0557.0675.1141.1517.0832.0871.0910.1064.0948.13310.2.0987.1293.1443.180821570.312171255.1368.1406.1772.1554.1915.1591.1950.16642019.17002054.173620880.4.1628.1844.18790,5.19852123219022240.622572517.2549238927042422273422912454248623242642235726730.72580261127642794282328520.828812910293929672995.30233051.3078.310631330.9.3159323832643389.33403577.3365.3599.31863212.3289.33151.0.3413.3438.3461.3485.35083531.355436211.1.3643.3665.36863708.3830.37293925.3749.3770379038103849.4032.3997.4162.401541771.2.38693888.4066.3907.40824236437039443962.39801.3.4049.4099.4115.413141471.44192.42074222.4251.4265.4279.4292.4306.43191.5.4332.4345.4357.4382439444064418.4429.4441.445244634474.4484451545451.61.7.4495.45054525.4535.45734656.4582.4664.4732.46334706.4454.4564.4591.4599.4608.4616.4625.4699.4649.47191.8464146714678.468646931.9.4713.4726.4738.4744.4750.4756.4761.47672.0.4772.4778.4783.4788.4793.4798.4803.4808.4812.48172.1.4821.4826.4830.48344838.4842.484648504854.48572.2486148644868.4871.4875.4878488148844887.4890.49044906.49292.3.4893.48964898.4901.4909.4911.4913.491649204940.4918.4922.4925.4927.4931.4932.49492.44934.49362,549384941.4943494549464948.4951.49522.64953.4955.4956.4957.49594960.4961.4962.49634964.4966.49704971.497249734965.497449812.7.4967.4968.4969.4974.49774979.498549892.8.4975.4976.4977.49784979.498049812.94982498249834984.49844985498649863.0.4987 .4987.49874988.4988.4989498949904990Note: This tablo gives the area in the right-hand tail of the distribution (1.e., Z 0). But since the normaldistribution is ymmetrical about Z=0, the area in the left-hand tail is the same as the area in the correspondingright-hand tail. For example, P-1.96 s Zs 0) = 0.4750. Thoroforo, PY-1.96 < Zs 1.96) = 2(0.4750) = 0.95.%3D%3D%3DCritical Values IZtabl0.100 Ztab-a0.0010.0050.0100.0250.050IZ tabl3.0902.5762.3261.9601.6451.282CS Scanned with CamScanner

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Description: Question FiveThe management of a supermarket wants to adopt a new promotional policy ofgiving free gift to every customer who spends more than a certain amount per visitat this supermarket. The expectation of the management is that after thispromoti

The amount is given by x = u + z0.1σ x = 400 + 1.282 x 30x = 438.46

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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 £?

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 £?

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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Concept explainers

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.

Topic Video

Question

TABLE D.1
AREAS UNDER THE STANDARDIZED NORMAL DISTRIBUTION
Example
Pr(0sZ 1.96) -0.4750
Pr(Z21.96) -0.5 - 0.4750 -0.025
0.4750
1.96
.00
.01
.02
.03
.04
.05
.06
.07
.08
.09
.0359
.0753
0160
.0279
.0319
.0714
.1103
.1480
.0080
.0120
.0517
.0199
.0596
.0239
0.0
1
0.1
.0000
.0398
.0793
.1179
.0040
.0636
.1026
.0438
.0478
.0557
.0675
.1141
.1517
.0832
.0871
.0910
.1064
.0948
.1331
0.2
.0987
.1293
.1443
.1808
2157
0.3
1217
1255
.1368
.1406
.1772
.1554
.1915
.1591
.1950
.1664
2019
.1700
2054
.1736
2088
0.4
.1628
.1844
.1879
0,5
.1985
2123
2190
2224
0.6
2257
2517
.2549
2389
2704
2422
2734
2291
2454
2486
2324
2642
2357
2673
0.7
2580
2611
2764
2794
2823
2852
0.8
2881
2910
2939
2967
2995
.3023
3051
.3078
.3106
3133
0.9
.3159
3238
3264
3389
.3340
3577
.3365
.3599
.3186
3212
.3289
.3315
1.0
.3413
.3438
.3461
.3485
.3508
3531
.3554
3621
1.1
.3643
.3665
.3686
3708
.3830
.3729
3925
.3749
.3770
3790
3810
3849
.4032
.3997
.4162
.4015
4177
1.2
.3869
3888
.4066
.3907
.4082
4236
4370
3944
3962
.3980
1.3
.4049
.4099
.4115
.4131
4147
1.4
4192
.4207
4222
.4251
.4265
.4279
.4292
.4306
.4319
1.5
.4332
.4345
.4357
.4382
4394
4406
4418
.4429
.4441
.4452
4463
4474
.4484
4515
4545
1.6
1.7
.4495
.4505
4525
.4535
.4573
4656
.4582
.4664
.4732
.4633
4706
.4454
.4564
.4591
.4599
.4608
.4616
.4625
.4699
.4649
.4719
1.8
4641
4671
4678
.4686
4693
1.9
.4713
.4726
.4738
.4744
.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
4906
.4929
2.3
.4893
.4896
4898
.4901
.4909
.4911
.4913
.4916
4920
4940
.4918
.4922
.4925
.4927
.4931
.4932
.4949
2.4
4934
.4936
2,5
4938
4941
.4943
4945
4946
4948
.4951
.4952
2.6
4953
.4955
.4956
.4957
.4959
4960
.4961
.4962
.4963
4964
.4966
.4970
4971
.4972
4973
4965
.4974
4981
2.7
.4967
.4968
.4969
.4974
.4977
4979
.4985
4989
2.8
.4975
.4976
.4977
.4978
4979
.4980
4981
2.9
4982
4982
4983
4984
.4984
4985
4986
4986
3.0
.4987 .4987
.4987
4988
.4988
.4989
4989
4990
4990
Note: This tablo gives the area in the right-hand tail of the distribution (1.e., Z 0). But since the normal
distribution is ymmetrical 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 s Zs 0) = 0.4750. Thoroforo, PY-1.96 < Zs 1.96) = 2(0.4750) = 0.95.
%3D
%3D
%3D
Critical Values IZtabl
0.100 Ztab-
a
0.001
0.005
0.010
0.025
0.050
IZ tabl
3.090
2.576
2.326
1.960
1.645
1.282
CS Scanned with CamScanner

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