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Magazine Chapter 5: Q. 82 (page 354)
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,
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