Question

The waiting times between a subway departure schedule and the arrival of a passenger are uniformly distributed between 0 and 5 minutes. Find the probability that a randomly selected passenger has a waiting time greater than 1.25 minutes.

Answer 1

Answer: 0.75

Step-by-step explanation:

Given : Interval for uniform distribution : [0 minute, 5 minutes]

The probability density function will be :-

$f(x)=\dfrac{1}{5-0}=\dfrac{1}{5}=0.2\ \ ,\ 0$

The probability that a given class period runs between 50.75 and 51.25 minutes is given by :-

$P(x>1.25)=\int^{5}_{1.25}f(x)\ dx\\\\=(0.2)[x]^{5}_{1.25}\\\\=(0.2)(5-1.25)=0.75$

Hence,  the probability that a randomly selected passenger has a waiting time greater than 1.25 minutes = 0.75