Question

The time(in minutes) until the next bus departs a major bus depot follows a distribution with \(f(x)=\frac{1}{20}\) where \(x\) goes from \(25\) to \(45\) minutes.

a. Define the random variable. \(X=\).

b. \(X~\)

c. Graph the probability distribution.

Short answer

Part a. \(X=\)The time (in minutes) until the next bus departs a major bus depot.

Part b. \(X~U(25,45)\)

Part c.

Step-by-step solution

Part a. Step 1. Explanation

The random variable,\(X\) can be defined as,

\(X=\)The time (in minutes) until the next bus departs a major bus depot.

Part b. Step 1. Explanation

According to given information the following data is given,

\(f(x)=\frac{1}{20},25<x<45\)

Density function is given below,

\(f(x)=\frac{1}{b-a},a<x<b\)

Therefore,

\(a=25\)

\(b=45\)

The random variable \(X\)is uniformly distribution is given by,

\(X~U(25,45)\)

Part c. Step 1. Explanation

Height of probability distribution is given by,

\(f(x)=\frac{1}{b-a}\)

\(f(x)=\frac{1}{45-25}\)

\(f(x)=\frac{1}{20}\)

Therefore height of distribution is \(\frac{1}{20}\)

The graph is given by,