Answer
It is appropriate to use a normal distribution as an approximation for the probability distribution of $x$ because the interval $(2.65,17.35)$ lies completely within the range from 0 to 25.
Work Step by Step
$q=1-p=1-.4=.6$
$\mu=25(.4)=10$
$\sigma=\sqrt {npq}=\sqrt {25(.4)(.6)}=2.45$
$\mu\pm3\sigma=10\pm3(2.45)=(2.65,17.35)$
