3. Entry-level job seekers want to estimate the proportion of entry-level job postings required three or more years of related work experience. A random sample of 220 entry-level job postings showed that 121 out of them require three or more years of related work experience.

(a) Construct a 97% confidence interval for the population proportion of all entry-level job postings which require three or more years of related work experience. Show your work by including a calculator menu you used, the values you entered into the menu, and the confidence interval.

(b) Interpret it in the content of the question.

(c) Suppose that entry-level job seekers want to construct 95% confidence interval that its estimate for the proportion is within 3.75% of the true proportion using the prior estimate of 55%. How large a sample of entry-level job postings is necessary? Show your work by including a formula and the values you used.