Answer
$4913\lt\mu\lt5087$
unbelievable. see explanations below.
Work Step by Step
Given $n=415,\bar X=5000,s=900,c=0.95$
At the 95% confidence, the critical z-value is $z_{\alpha/2}=1.96$
and the error of estimation can be
found as $E=1.96\times\frac{600}{\sqrt {415}}=86.6$
Thus, the interval of the mean can be found as
$\bar X−E\lt\mu\lt\bar X+E$ which gives $4913\lt\mu\lt5087$
If a father claimed that his children watched 4000 hours, the number
would fall far below the estimated range and regarded as unbelievable.