To find the normal price of the mini-fridge, we can set up an equation based on the information given. The warranty costs $41.25, which is 12.5% of the mini-fridge's normal price.
Let \( x \) be the normal price of the mini-fridge. Then we can write the equation:
\[ 0.125x = 41.25 \]
To find \( x \), divide both sides by 0.125:
\[ x = \frac{41.25}{0.125} \]
Calculating the right-hand side:
\[ x = 330 \]
Thus, the cost of the mini-fridge, to the nearest dollar, is \( \boxed{330} \).