Are you a chocolate "purist," or do you like other ingredients in your Chocholate? American Demographics reports that almost 75% of consumers like the traditional ingredients such as nuts or caramel in their chocolate. They are less enthusiastic about the taste of mint or coffee that provide more distinctive flavors. A random sample of 200 consumers is selected and the number who like nutes or caramel in their chocholate is recorderd.
a) What is the approximate sampling distribution for the sample proportion ρ^? What are the mean and standard deviation for this distribution?
b) What is the probability that the sample percentage is greater than 80%?
c) Within what limits would you expect the sample propotion to lie about 95% of the time?