題組內容

II. (30%) A pollster plans to randomly select people and ask about their party affiliation. The respondent can choose to be identified with one of the four political parties: Party A, B, C, or D. The pollster is interested to know \( p_A \), the share of population that are leaning toward Party A.

(a) Describe the probability distribution of \( P_A \), the proportion of respondents who was identified with Party A in the sample. Explain whether normal distribution is appropriate to approximate the distribution of \( P_A \).