The time of travel from a person's apartment to the bus station follows a uniform distribution over the interval from 20 to 30 minutes.If he/she leaves home at 9:05 AM,what is the probability that he/she will get to the station between 9:25 and 9:30 AM?
A)1.0
B)0
C)0.5
D)0.25

Question

Quizplus · Accepted Answer

The total time interval from 9:05 AM to 9:30 AM is 25 minutes.
The probability that the person can reach the bus station between 9:25 and 9:30 AM is the same as the probability that the travel time is between 20 and 25 minutes.
The probability of this happening can be calculated as the ratio of the length of the interval [20,25] to the length of the entire interval [20,30]:
P(20 ≤ X ≤ 25) = (25-20)/(30-20) = 0.5

The Time of Travel from a Person's Apartment to the Bus