The United States Centers for Disease Control and Prevention (CDC) found that 17.9% of women ages 12–59 test seropositive for HPV‑16. Suppose that Tara, an infectious disease specialist, assays blood serum from a random sample of n=1000 women in the United States aged 12-59.
Apply the central limit theorem for the distribution of a sample proportion to find the probability that the proportion, ^ p , of women in Tara's sample who test positive for HPV‑16 is greater than 0.202 . Express the result as a decimal precise to three places.