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 0.1990.199. 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 HPV‑16 is less than 0.1740.174. Express the result as a decimal precise to three places.

P(^p<0.174)=

Answer 1

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

P( >0.199 ) = 1 - P( < 0.199)

= 1 - P(( - ) / < (0.199 -0.179) / 0.0121)

= 1 - P(z <1.65 )

Using z table

= 1 -0.9505

=0.0495

probability=0.050

(B)P( <0.174 ) =

= P[( - ) / < (0.174 - 0.179) /0.0121]

= P(z <-0.41 )

Using z table,   

= 0.3409

probability=0.341