Question

According to a study, 42% of adult Americans believe that marriage is now obsolete.

a) Suppose that a random sample of 500 adult Americans is asked whether marriage is obsolete. Describe the sampling distribution.

b) what is the probability that in a random sample of 500 adult Americans between 30% to 45% believe that marriage is obsolete?

Answer 1

Solution

Given that,

p = 0.42

1 - p = 1 - 0.42 = 0.58

n = 500

a)   = p = 0.42

  [p ( 1 - p ) / n] = [(0.42 * 0.58) / 500 ] = 0.0221

b) P(0.30 < < 0.45 )

= P[(0.30 - 0.42) / 0.0221 < ( - ) / < (0.45 - 0.42) / 0.0221]

= P(-5.43 < z < 1.36)

= P(z < 1.36) - P(z < -5.43)

Using z table,   

= 0.9131 - 0

= 0.9131