Answer
$3840\lt\mu\lt4134$
3840 dollars.
Work Step by Step
Given $n=50, \bar X=3987, \sigma=630$,
at a 90% confidence, the critical z-value is $z_{\alpha/2}=1.645$ and
the error of estimation can be found as $E=1.645\times\frac{630}{\sqrt {50}}=146.56$
the interval of the mean can then be found as
$\bar X−E\lt\mu\lt\bar X+E$ which gives $3840\lt\mu\lt4134$
If a day care center were starting up and wanted to
keep tuition low, a reasonable amount to charge would be 3840 dollars.
