Tests have shown that consumers generally tend to agree on the strength of various fragrances, butthey are far less likely to agree on preferences. Suppose that 58 consumers are randomly selected andtested regarding their preference between the fragrances CK One and Chanel No. 5. Suppose thatthere is no difference in preference regarding the two fragrances among the general public, i.e. halfof all consumers prefer CK One to Chanel No. 5 and the other half prefer Chanel No. 5 to CK One.

(a) What is the sampling distribution of the proportion of tested consumers who prefer Chanel toCK?

(b) What is the probability that fewer than 30% of the tested consumers state a preference forChanel?

(c) How large does the sample have to be for the standard deviation of the sample mean to be0.015?