The duration of the class is uniformly distributed with a minimum of 50.0 minutes and a maximum of 52.0 minutes. This means the random variable for class duration [tex]X[/tex] has density function
[tex]f_X(x)=\begin{cases}\dfrac1{52.0-50.0}=\dfrac12&\text{for }50.0\le x\le52.0\\[1ex]0&\text{otherwise}\end{cases}[/tex]
You're looking for the probability that the class runs less than 51.5 minutes, or [tex]\mathbb P(X<51.5)[/tex], which is given by the integral
[tex]\displaystyle\mathbb P(X<51.5)=\int_{-\infty}^{51.5}f_X(x)\,\mathrm dx=\frac12\int_{50.0}^{51.5}\mathrm dx=\frac{51.5-50.0}2=0.75[/tex]
