A survey indicates that 26% of consumers from a certain region are willing to sp

Question

A survey indicates that

26%

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

100

consumers from the region is selected. Ifpossible, use the normal distribution to approximate the sampling distribution of the proportion. Complete parts (a) through(g) below.

what is the probability that in the sample between

23%

and

29%

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

Explanation / Answer

p = 0.26

n = 100

mean = 0.26

sd =sqrt(pq/n) = sqrt(0.26*0.74/100) = 0.043863

Z = (p - 0.26)/0.043863

P(0.23 < p < 0.29)

=P ( 0.68<Z<0.68 )

=0.5034

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