7.56 Oh, Nuts! Are you a chocolate "purist," or do you like other ingredients in your chocolate? American Demographics reports that almost 75% of consum- ers like traditional ingredients such as nuts or caramel in their chocolate. They are less enthusiastic about the taste of mint or coffee that provide more distinc- tive flavours. 18 A random sample of 200 consumers is selected and the number who like nuts or caramel in their chocolate is recorded.

a. What is the approximate sampling distribution for the sample proportion p? What are the mean and standard deviation for this distribution?

b. What is the probability that the sample proportion is greater than 80%?

c. Within what limits would you expect the sample proportion to lie about 95% of the time?