Answer: 0.5357
Step-by-step explanation:
If a continuous random variable x is distributed uniformly in interval [a,b] , then the probability density function is given by :-
[tex]f(x)=\dfrac{1}{b-a}[/tex]
Given : The waiting times between a subway departure schedule and the arrival of a passenger are uniformly distributed between 0 and 7 minutes.
Probability density function=[tex]f(x)=\dfrac{1}{7-0}=\dfrac{1}{7}[/tex]
Now, the probability that a randomly selected passenger has a waiting time greater than greater than 3.253.25 minutes :-
[tex]\int^{7}_{3.25}\ f(x)\ dx\\\\= \dfrac{1}{7}\int^{7}_{3.25}\ dx\\\\ \dfrac{1}{7}[x]^{7}_{3.25}\\\\=\dfrac{1}{7}[7-3.25]=\dfrac{3.75}{7}=0.535714285\approx0.5357[/tex]
Hence, the required probability = 0.5357
