Answer
a) $0.5239$
b) $0.8944$
c) Yes
Work Step by Step
a) We first find the value of z:
$z=\frac{0.8565−0.8535}{0.0518/\sqrt1}=0.06$
Using the table of z-values, we see that the probability is $0.5239$.
b) $z=\frac{0.8565−0.8535}{0.0518/\sqrt{465}}=1.25$
Using the table of $z$-values, we see that the probability is $0.8944$.
c) Yes, since the rate is almost $90$ %, it seems that the claim is fair.