In order to gain additional information about respondents, some marketing resear

Question

In order to gain additional information about respondents, some marketing researchers have used ultraviolet ink to precode questionnaires that promise confidentiality to respondents. Of 253 randomly selected marketing researchers who participated in an actual survey, 168 said that they disapprove of this practice. Suppose that, before the survey was taken, a marketing manager claimed that at least 76 percent of all marketing researchers would disapprove of the practice. (a) Assuming that the manager's claim is correct, calculate the probability that 168 or fewer of 253 randomly selected marketing researchers would disapprove of the practice. Use the normal approximation to the binomial.

Explanation / Answer

here mean =np =253*0.76 =192.28

std deviation =(np(1-p))1/2 =6.7932

hence probability that 168 or fewer of 253 randomly selected marketing researchers would disapprove of the practice =P(X<=168)=P(Z<(168.5-192.28)/6.7932)=P(Z<-3.5006)=0.0002

please reply for any explanation needed.

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