Answer
$P(0.25\lt p ̂\lt 0.3)=0.6635$
Work Step by Step
25% = 0.25 and 30% = 0.3
$P(0.25\lt p ̂\lt 0.3)=P(\frac{0.25-0.29}{{\sqrt {\frac{0.29(1-0.29)}{500}}}}\lt z\lt\frac{0.3-0.29}{{\sqrt {\frac{0.29(1-0.29)}{500}}}})=P(-1.97\lt p ̂\lt0.49)=P(p ̂\lt0.49)-P(p ̂\lt-1.97)=0.6879-0.0244=0.6635$
