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(Z z1.96) -0.5-0.4750 -0.0250.47501.9600.01.02.03.04.05.06.07.08.090.0.0000.0398.0040.0080.0120.0517.01600199.0239.0279.0675.0319.03590.1.0438.0478.0596.0987.1368.1736.0636.1026.1406.17722123.0557.0714.07530.2.0793.0832.0871.1255.0910.0948.13311700.1064.1103.1480.18442190.11410.3.1179.1554.1915.12171293.1443.18082157.15170.4.1591.1628.1664.187922240.5.1950.19852019205420880.622572580229123242642235723892422245424862517254928520.72611.2673270427342764279428230.828812910293929673051331535542995.3023.3078.3133338931060.93159.3413.3186.3438.32123238326432893340.33651.0.34613485.350835313577359936211.1.3643.3665.3686.3708.3729.374937703790.381038301.2.3849.3869404938883907392539443962.39804147.399740151.3.40324066.4082.4099.41154131416241771.4.4192.42074222423642514265439442794292430643191.5.4332.43454357.4370438244064418442944411.6.445244634474.4484449545054515460845254616.4535462545451.7.4454.45644582466445734591.459946331.8.46494719.464146714738470647674656467846864693.46991.9.47134726.473247444750.4756.47612.0.4772.4778.4783.4788.4793.4798480348084812.48172.1.4821.4826.4830.4834483848424846.48504854.48572.2.4861.486448714901486848784890491648754881488448872.3.489348964898490449134934.495149064909.49112.4.4918.4920.4940.49224941492549274929.4931493249362.5.49384943.49454946.49484949.4952.4955.49662.6.49534956496449744957495949604961496249632.7.4965.4967.4968.496949704971497249732.8.4974.49754976497749774979.49784984497949854980498149862.9.49814982.498249834984.498549863.0.498749874987.4988.49884989498949894990A990Note: This table gives the area in the right-hand tail of the distribution (1.e., Z 0). But since the normaldistribution is symmetrical about Z=0, the area in the left-hand tail is the same as the area in the correspondingright-hand tail. For example, A-1.96 s Zs 0) = 0.4750. Therefore, P(-1.96 s Zs 1.96)- 2(0.4750) 0.95.tab =cs Scanned with CamScanner

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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 £?

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 £?

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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