Answer
$1.54$ cm
Work Step by Step
We need to sketch this problem.
As we see in the sketch below, the plastic is a spherical refracting surface.
In such surfaces, we know that
$$\dfrac{n_1}{s}+\dfrac{n_2}{s'}=\dfrac{n_2-n_1}{R}$$
We are treating the bubble as a point source, as seen below.
Since $s$ faces the concave side of the refracting surface, $R=-R_{\rm ball}=-4$ cm.
Solving for $s'$,
$$ \dfrac{n_2}{s'}=\dfrac{n_2-n_1}{R}-\dfrac{n_1}{s}$$
$$ s' =n_2\left[\dfrac{n_2-n_1}{R}-\dfrac{n_1}{s}\right]^{-1}$$
Plugging the known;
$$ s' =(1)\left[\dfrac{1-1.59}{-4}-\dfrac{1.59}{2}\right]^{-1}=\color{red}{\bf -1.54}\;\rm cm$$
The air bubble appears to be under the surface of the plastic ball by a distance of 1.5 cm.
