Buses arrive and depart from a college every 20 minutes.The probability density function for the waiting time t (in minutes)for a person arriving at the bus stop is on the interval Find the probability that the person will wait no longer than 5 minutes.
A)
B)
C)
D)
E)

Question

​Buses arrive and depart from a college every 20 minutes.The probability density function for the waiting time t (in minutes)for a person arriving at the bus stop is  on the interval  Find the probability that the person will wait no longer than 5 minutes. ​
A) ​ 
B) ​ 
C) ​ 
D) ​ 
E) ​

Quizplus · Accepted Answer

To find the probability that the person will wait no longer than 5 minutes, we need to integrate the given probability density function from 0 to 5 minutes.

P(t ≤ 5) = ∫0^5 11e^(-t/20) dt

Using integration by substitution, let u = -t/20, du/dt = -1/20, dt = -20 du.

P(t ≤ 5) = ∫u=-5/20u=0 11e^u (-20 du)

P(t ≤ 5) = 11[(-e^(-5/20)) - (-e^0)]

P(t ≤ 5) = 11(1 - e^(-1/4))

P(t ≤ 5) ≈ 0.7169

Rounded to four decimal places, the answer is 0.7169, which corresponds to choice C.

​Buses Arrive and Depart from a College Every 20 Minutes

Buses Arrive and Depart from a College Every 20 Minutes