#### Answer

$[76.5,106.5)$

#### Work Step by Step

Consider the average of all the scores.
$80 \leq \dfrac{82+75+80+90+2x}{5} \lt 90$
This implies $(80)(5) \leq 327+2x \lt (90)(5)$
or, $400 \leq 327+2x \lt 450$
or, $76.5 \leq x \lt 106.5$
Our result is: $[76.5,106.5)$