#### Answer

The least amount of percentage is $95$%

#### Work Step by Step

First, let $x$ be the grade on the final examination.
Then from the asked problem we have the inequality:
$ \frac{0.86+0.88+0.92+0.84+2x}{6} \geq 0.90$
Next, all we have to do is solve the inequality.
$ \frac{0.86+0.88+0.92+0.84+2x}{6} \geq 0.90$
$ \frac{3.50+2x}{6} \geq 0.90$
Multiply with $6$ on both sides.
$ \frac{3.5+2x}{6}\times6 \geq 6\times0.90$
$ 3.50+2x \geq 5.40$
Subtract $3.50$ on both sides.
$ 3.50+2x-3.50 \geq 5.40-3.50$
$ 2x \geq 1.9$
Divide with $2$ on both sides.
$ \frac{2x}{2} \geq \frac{1.9}{2}$
$ x \geq 0.95$
Which is our solution.