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the United States Centers for Disease Control and Prevention (CDC) found that 17

ID: 3062645 • Letter: T

Question

the United States Centers for Disease Control and Prevention (CDC) found that 17.9% of women ages 12–59 test seropositive for HPV16. 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 HPV16 is greater than 0.199. Express the result as a decimal precise to three places.

P(p >0.199)=

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 HPV16 is less than 0.174. Express the result as a decimal precise to three places.

P(p <0.174)=

Explanation / Answer

n =1000 , p = 0.179

P(pcap > 0.199)

z = (pcap - p ) / sqrt ( p * (1 - p) / n)
= ( 0.199 - 0.179) / sqrt( 0.179 * 0.821/1000)
= 1.6498
P(pcap > 0.199) = P (z > 1.6498) = 0.049


P(pcap < 0.174)
z = (pcap - p ) / sqrt ( p * (1 - p) / n)
= ( 0.174 - 0.179) / sqrt( 0.179 * 0.821/1000)
= -0.4125

P(pcap < 0.174) = P (z <-0.4125) = 0.339