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 ?=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, ?̂, of women in Tara's sample who test positive for HPV‑16 is greater than 0.206. Express the result as a decimal precise to three places. Apply the central limit theorem for the distribution of a sample proportion to find the probability that the proportion of women in Tara's sample who test positive for HPV‑16 is less than 0.169. Express the result as a decimal precise to three places.

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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 ?=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, ?̂, of women in Tara's sample who test positive for HPV‑16 is greater than 0.206. Express the result as a decimal precise to three places.

Apply the central limit theorem for the distribution of a sample proportion to find the probability that the proportion of women in Tara's sample who test positive for HPV‑16 is less than 0.169. Express the result as a decimal precise to three places.

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