Answer
$P(40 \leq p̂ \leq 45) = 0.3232$. This implies that about 32 out of 100 samples of size n = 500 adult Americans will have 40%-45% individuals who believe that marriage is now obsolete.
Work Step by Step
Using data from part a for $40 \leq p̂ \leq 45$, we have:
$z = \frac{0.40 - 0.39}{0.022} = 0.45$
$z = \frac{0.45 - 0.39}{0.022} = 2.73$
$P(40 \leq p̂ \leq 45) = P(0.45 < z < 2.73) = P(z < 2.73) - P(z < 0.45)$
= 0.9968 - 0.6736 = 0.3232
