Answer
The probability of finding the electron in the range $dx$ at $x = L/2$ is 0.
Work Step by Step
The normalized wave function given in exercise 7B.3 is $({2\over L})^{1/2}sin({2πx\over L})$
The probability of finding a particle over a point is always zero.
To proof that consider a wave function $\psi(x)$ where is based on one dimension.
$P = \int_{x_0}^{x_0+dx} \psi ^2 dx$
Which is clearly 0 as $dx$ is tending to 0.
