A public health screening program will estimate the proportion of Perth women aged 16-24 who have a human papillomavirus (HPV) infection. (There are nearly 200 types of HPV, most of which cause no symptoms in most people.) A random sample of 1,437 Perth women in this age group was selected.

a. If the population proportion of women carrying HPV were 19%, what is the chance that the sample proportion could exceed 20% in a random sample of this size?

b. 253 of the women in the sample were found to be HPV carriers. Calculate a 90% confidence interval for the proportion of Perth women aged 16-24 who have an HPV infection.

Thank you