Question

find the probability of selecting a class that runs greater than 51.5, uniformly distributed between 46.0 and 56.0

Answer 1

Let \(X\) the random variable for this situation.

Then the probability density is given by
\[f_X(x)=\begin{cases}\dfrac{1}{56-46}=\dfrac{1}{10}&\text{for }46\le x\le56\\\\0&\text{elsewhere}\end{cases}\]
Desired probability:
\[P(X>51.5)=\int_{51.5}^{56}f(x)~dx=\frac{1}{10}(56-51.5)=0.45\]