need help with math hw

Question

in a​ poll, 51​% of the people polled answered yes to the question​ "Are you in favor of the death penalty for a person convicted of​ murder?" The margin of error in the poll was 2​%, and the estimate was made with 96​%

confidence. At least how many people were​ surveyed?

he minimum number of surveyed people was___

round to the nearest integer

Answer 1

margin of error = z critical * sqrt(phat*(1-phat)/n)

z*critical * sqrt(phat*(1-phat)/n) <= 0.02

square both sides

z*critical^2 * (phat*(1-phat)/n) <= 0.02^2

multiply both sides by n

z*critical^2 * (phat*(1-phat)) <= 0.02^2 * n

divide both sides by 0.02^2

z*critical^2 * (phat*(1-phat)) <= n

--------------

0.02^2

z*critical for 96% confidence, is upper 0.02 tail (0.98 probability) = 2.05

phat = 0.51, 1-phat = 0.49

2.05^2 * (0.51*0.49)

--------------------------- <= n

0.0004

2625.51 <= n

n = 2626