Question

Suppose 44% of American singers are Grammy award winners.

If a random sample size 721 is selected, what is the probability that the proportion of Grammy award winners will differ from the singers proportion by greater than 5%? Round your answer to four decimal places.

Answer 1

Solution

=  [p( 1 - p ) / n] = [(0.44 * 0.56) / 721] = 0.0185

P(differ from the singers proportion by greater than 5%)

= 1 - P[ -0.05 / 0.0185 < ( - ) / < 0.05 / 0.0185]

= 1 - P(-2.70 < Z < 2.70)

= 1 - 0.9931

= 0.0069