To find out how far Amy ran each day, divide the total distance she ran by the number of days.
The total distance is \(3 \frac{1}{4}\) miles, which can be converted to an improper fraction:
\[ 3 \frac{1}{4} = \frac{13}{4} \text{ miles} \]
Now, divide this by 4 (the number of days):
\[ \text{Distance per day} = \frac{\frac{13}{4}}{4} = \frac{13}{4} \times \frac{1}{4} = \frac{13}{16} \text{ miles} \]
So, Amy ran \(\frac{13}{16}\) miles each day.