Question

the waiting times between a subway departure schedule and the arrival of a passenger are uniformly distributed between 0 and 9 minutes. find the probability that a randomly selected passenger has a waiting time less than 0.75 minutes. find the probability that a randomly selected passenger has a waiting time less than 0.75 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 \(f(x)=\frac{1}{b - a}\) for \(a\leq x\leq b\). The probability \(P(c<X<d)\) is given by \(\frac{d - c}{b - a}\), where \(a = 0\), \(b=9\), \(c = 0\), \(d = 0.75\).

Step2: Calculate the probability

Substitute the values into the formula: \(\frac{0.75-0}{9 - 0}=\frac{0.75}{9}\).

$$ \frac{0.75}{9}=0.0833\cdots $$

Rounding to three decimal places.

Answer:

\(0.083\)