Question

Suppose 56% of the population are more than 6 feet tall.

If a random sample of size 643 is selected, what is the probability that the proportion of persons more than 6 feet tall will differ from the population proportion by more than 5%? Round your answer to four decimal places.

Answer 1

Solution

Given that,

=  [p ( 1 - p ) / n] = [(0.56 * 0.44) / 643 ] = 0.0196

= 1 - P[(-0.05) / 0.0196 < ( - ) / < (0.05) / 0.0196]

= 1 - P(-2.55 < z < 2.55)

= 1 - P(z < 2.55) - P(z < -2.55)

= 1 - P(0.9946 - 0.0054)

= 1 - 0.9892

= 0.0108

Probability = 0.0108