Question

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,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.

?(?̂ >0.202)=

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

?(?̂ <0.172)=

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( > 0.202) = 1 - P( < 0.202)

= 1 - P(( - ) / < (0.202 - 0.179) / 0.0121)

= 1 - P(z < 1.90)

Using z table

= 1 - 0.971

= 0.029

b) P( < 0.172)

= P[( - ) / < (0.172 - 0.179) / 0.0121]

= P(z < -0.58)

Using z table,

= 0.281