(h) A company sends its catalog to 20000 of its regular customers and they estim

Question

(h) A company sends its catalog to 20000 of its regular customers and they estimate that each will will order something with probability 50%. The amount of each order is random and it is esti- i. Find the expected value and standard deviation of the total sales generated from sending the ii. Now, in addition, they also send catalogs to 10000 potential customers and expect that 5% mated that it has an average of $200 and standard deviation $100. catalog to regular customers will make an order. Find expected value of the total amount of sales (from both regular and new customers) iii. Extra credit: find standard deviation of the amount of total sales. Explain how you got your answer, and justify your steps.

Explanation / Answer

following information has been given

(i) Expected sell=20000*0.5*200=2000000

standard deviation=20000*0.5*100=1000000

expected sell=n*mean*p and sd(sell)=n*sd*p

(ii) expected sell=20000*0.5*200+10000*0.05*200=2100000

in this case E(sell)=n1*mean(x1)*p1+n2*mean(x2)*p2

(iii) variance of total=(20000*0.5*100)2+(10000*0.05*100)2=

=(20000*0.5*100)*(20000*0.5*100)+(10000*0.05*100)*(10000*0.05*100)

standard deviation of total =sqrt(variance(total))=

=sqrt((20000*0.5*100)*(20000*0.5*100)+(10000*0.05*100)*(10000*0.05*100))=101249

variance(a*x1+b*x2)=a*a*var(x1)+b*b*var(x2)

variance=sd*sd

n mean sd p regular(x1) 20000 200 100 0.5 new(x2) 10000 200 100 0.05

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