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 232 randomly selected marketing researchers who participated in an actual survey, 160 said that they disapprove of this practice. Suppose that, before the survey was taken, a marketing manager claimed that at least 67 percent of all marketing researchers would disapprove of the practice.

(a) Assuming that the manager's claim is correct, calculate the probability that 160 or fewer of 232 randomly selected marketing researchers would disapprove of the practice. Use the normal approximation to the binomial. (Round z value to 2 decimal places. Round your answer to 5 decimal places.)

P(x 160)

Explanation / Answer

Ans:

Normal approximation to the Binomial distribution:

n=232

p=0.67

mean=np=155.44

standard deviation=sqrt(232*0.67*(1-0.67))=7.162

z=(160-155.44)/7.162=0.64

P(X<=160)=P(z<=0.64)=0.73891

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