Buses arrive at a specified stop at 15-minute intervals starting at 7A. M. That is, they arrive at 7, 7:15 ,7:30 ,7:45,and so on.
a) If a passenger arrives at the stopat a time that is uniformly distributed between 7 and 7:30, find the probability that he waits(a) less than 5 minutes for a bus;(b) more than 10 minutes for a bus

a)  P=1/3

b)  P=1/3

Step-by-step explanation:

We know that buses arrive at a specified stop at 15-minute intervals starting at 7A.M. Therefore,  ,they arrive at 7, 7:15 ,7:30 ,7:45,and so on.

a) We calculate the probability that a passenger waits less than 5 minutes for a bus between 7 and 7:30. We know that  a passenger arrives at the stopat a time that is uniformly distributed between 7 and 7:30, we have:

We conclude that the passenger will wait less than 5 minutes for a bus if he arrives between 7:10 and 7:15, or between 7:25 and 7:30. We get:

Therefore, the probability is P=1/3.

b) We conclude that the passenger will wait more than 10 minutes for a bus if he arrives between 7:00 and 7:05, or between 7:15 and 7:20. We get:

Therefore, the probability is P=1/3.

wheres graph

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