Answer
To satisfy the fluctuations of $I$, $R$ needs to lie in the interval $[23.5294,24.4898]$.
Work Step by Step
The exercise challenges us to find the interval of $R$ on which $I$ would be within $0.1$ amp of the value $I_0=5$. In other words, $$|I-5|\le0.1$$
We are also given the Ohm's law: $V=IR$, and $V=120$ volt. That means we can rewrite $I=120/R$.
Now the inequality would become $$|\frac{120}{R}-5|\le0.1$$
To find the interval, we need to solve the inequality: $$-0.1\le\frac{120}{R}-5\le0.1$$ $$4.9\le\frac{120}{R}\le5.1$$ $$\frac{120}{4.9}\ge R\ge\frac{120}{5.1}$$ $$24.4898\ge R\ge23.5294$$
So to satisfy the fluctuations of $I$, $R$ needs to lie in the interval $[23.5294,24.4898]$.
