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}\frac1{52.0-50.0}=\frac12&\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`