Question

The United States Centers for Disease Control and Prevention (CDC) found that 17.9%17.9% of women ages 1212–5959 test seropositive for HPV‑16. Suppose that Tara, an infectious disease specialist, assays blood serum from a random sample of n=1000n=1000 women in the United States aged 1212–59.59.

Apply the central limit theorem for the distribution of a sample proportion to find the probability that the proportion, ^p,p^, of women in Tara's sample who test positive for HPV‑16 is greater than 0.2010.201. Express the result as a decimal precise to three places.

P(^p>0.201)=P(p^>0.201)=

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 0.1730.173. Express the result as a decimal precise to three places.

P(^p<0.173)=P(p^<0.173)=

Answer 1

Solution

Given that,

p = 0.179

1 - p = 1 - 0.179 = 0.821

n = 1000

= p = 0.179

=  [p( 1 - p ) / n] = [(0.179 * 0.821) / 1000 ] = 0.0121

a) P( > 0.201) = 1 - P( < 0.201 )

= 1 - P(( - ) / < (0.201 - 0.179) / 0.0121 )

= 1 - P(z < 1.82)

Using z table

= 1 - 0.966

= 0.034

b) P( < 0.173)

= P[( - ) / < (0.173 - 0.179) / 0.0121]

= P(z < -0.50)

Using z table,

= 0.309