Answer
$[76,126)$
Work Step by Step
Consider the average of all the scores.
$80 \leq \dfrac{70+75+87+92+x}{5} \lt 90$
This implies $(80)(5) \leq 324+x \lt (90)(5)$
or, $400 \leq 324+x \lt 450$
or, $76 \leq x \lt 126$
Our result is: $[76,126)$
