Answer
It is appropriate to use a normal distribution because the interval $(16.37,32.63)$ lies completely within the range from 0 to 35.
Work Step by Step
$q=1-p=1-.7=.3$
$\mu=35(.7)=24.5$
$\sigma=\sqrt {npq}=\sqrt {35(.7)(.3)}=2.71$
$\mu\pm3\sigma=24.5\pm3(2.71)=(16.37,32.63)$
