Question

Suppose 53% of American singers are Grammy award winners. If a random sample of size 834 is selected, what is the probability that the proportion of Grammy award winners will differ from the singers proportion by less than 4%? Round your answer to four decimal places.

Answer 1

P(Grammy award winner), p = 0.53

Sample size, n = 834

P( < A) = P(Z < (A - )/)

= p = 0.53

=

=

= 0.0173

P(the proportion of Grammy award winners will differ from the singers proportion by less than 4%) = P(-0.04/ < Z < 0.04/)

= P(-0.04/0.0173 < Z < 0.04/0.0173)

= P(-2.31 < Z < 2.31)

= P(Z < 2.31) - P(Z < -2.31)

= 0.9896 - 0.0104

= 0.9792