In June 2001, a referendum was held in North Dakota. The question was whether to

Question

In June 2001, a referendum was held in North Dakota. The question was whether to reverse a previous legislative action which allowed banking companies to employ an opt-out policy regarding their right to sell or otherwise make available information about customers to other companies. An opt-out policy basically forces the customers to actively ask not to have their information distributed by the bank. An opt-in policy forces the banks to ask for permission and not to distribute information unless the customer explicitly says it is okay. In the vote, the legislative action was overturned on s vote of 70% in favor of going back to the previous opt-in law. This action was, to say the least, disappointing to the banks. Suppose the views of the voters of North Dakota are in fact fairly universal, and that a SRS of 2000 people are Interviewed. What is the expected number of respondents who will agree with the banks? What is the variance? What is the probability that at least 1350 of the respondents will side with the majority of the voters of North Dakota?

Explanation / Answer

here p=0.3 ; n=2000

a) here expected number =np=2000*0.3=600

and varaicne =(np(1-p))=420

std deviation =20.4939

b)P(X>=1350) =1-P(X<=1349)=1-P(Z<(1349.5-1400)/20.4939)=1-P(Z<-2.46415)=1-0.0069 =0.9931

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