A survey indicates that 23 % of consumers from a certain region are willing to s

Question

A survey indicates that 23 % of consumers from a certain region are willing to spend extra for products and services from socially responsible companies. The researchers define these consumers as socially conscious consumers. According to one of the researchers, marketers need to know who these consumers are if they want to maximize the social and business return of their cause-marketing efforts. Suppose a sample of 200 consumers from the region is selected. If possible, use the normal distribution to approximate the sampling distribution of the proportion.

What is the probability that in the sample between

18 and 28 % are willing to spend extra for products and services from socially responsible companies

Explanation / Answer

Ans:

Normal approximation:

mean=0.23

standard error=sqrt(0.23*(1-0.23)/200)=0.0298

z(0.18)=(0.18-0.23)/0.0298=-1.68

z(0.28)=(0.28-0.23)/0.0298=1.68

P(-1.68<=z<1.68)=P(-1.68<=z<=1.68)=0.9535-0.0465=0.9070

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