Question

Suppose 55% of the population has a college degree. If a random sample of size 496 is selected, what is the probability that the proportion of persons with a college degree will differ from the population proportion by greater than 4%? Round your answer to four decimal places.

Answer 1

Using central limit theorem,

P( < p )= P(Z < ( - p) / sqrt ( p ( 1 - p) / n) ]

We have to calculate

P(p -0.04 < < p + 0.04) = P( 0.55 -0.04 < < 0.55 + 0.04)

= P( 0.51 < < 0.59)

= P( < 0.59) - P( < 0.51)

= P( Z < ( 0.59 - 0.55) / sqrt ( 0.55 * ( 1 - 0.55) / 496) - P( Z < ( 0.51 - 0.55) / sqrt ( 0.55 * ( 1 - 0.55) / 496)

= P(Z < 1.79) - P(Z < -1.79)

= 0.9633 - 0.0367

= 0.9266