Question

Please help answer statistics question? Statistics professor plans classes so carefully that the lengths of her classes are uniformally distributed between 50.0 and 52.0 minutes. Find the probability that a given class period runs LESS than 51.5 minutes.
Find the probability of selecting a class that runs less than 51.5 min.

(Type an integer or...; Please show steps HOW to get the answer! Thanks!; This is ONLY one question that I don't get.

Answer 1

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 $X$ has density function

$f_X(x)=\begin{cases}\dfrac1{52.0-50.0}=\dfrac12&\text{for }50.0\le x\le52.0\\[1ex]0&\text{otherwise}\end{cases}$

You're looking for the probability that the class runs less than 51.5 minutes, or $\mathbb P(X<51.5)$, which is given by the integral

$\displaystyle\mathbb P(X<51.5)=\int_{-\infty}^{51.5}f_X(x)\,\mathrm dx=\frac12\int_{50.0}^{51.5}\mathrm dx=\frac{51.5-50.0}2=0.75$