Find the average ordinate for the function in the given interval: $y=\sqrt[\phantom{2}]{3x1}$ from $x=1$ to $x=5.$ Round your answer to three significant digits.

$($A$)3\mathrm{.}11$

$4\mathrm{.}49$

$5\mathrm{.}38$

$1\mathrm{.}03$