Question

the waiting times between a subway departure schedule and the arrival of a passenger are uniformly distributed between 0 and 8 minutes. find the probability that a randomly selected passenger has a waiting time greater than 3.25 minutes.
find the probability that a randomly selected passenger has a waiting time greater than 3.25 minutes.
(simplify your answer. round to three decimal places as needed.)

Explanation:

Step1: Determine the formula for uniform distribution probability

For a uniform distribution \(U(a,b)\), the probability density function is \(f(x)=\frac{1}{b - a}\), and the probability \(P(X>x)=\frac{b - x}{b - a}\), where \(a = 0\), \(b = 8\), and \(x = 3.25\).

Step2: Substitute the values into the formula

Substitute \(a = 0\), \(b = 8\), and \(x = 3.25\) into \(P(X>x)=\frac{b - x}{b - a}\). We get \(P(X>3.25)=\frac{8 - 3.25}{8-0}\).

Step3: Calculate the result

First, calculate \(8 - 3.25=4.75\). Then \(\frac{4.75}{8}=0.59375\approx0.594\)

Answer:

\(0.594\)