Question

An airport provides complimentary shuttle bus service to downtown for arriving passengers. Passengers arrive randomly at the shuttle pick up location. The shuttle picks up passengers exactly every 35 minutes. Therefore, the time that a passenger will need to wait for the shuttle is uniformly distributed between 0 minutes to 35 minutes.

a. What is the probability that a random passenger will need to wait between 15 minutes and 30 minutes? Round your answer to three decimal places. Probability = ?

b. What is the probability that a random passenger will need to wait more than 15 minutes? Round your answer to three decimal places. Probability = ?

c. What is the probability that a random passenger will need to wait less than 18 minutes? Round your answer to three decimal places. Probability = ?

Answer 1

Solution:

X follows Uniform(a = 0 , b = 35)

a) What is the probability that a random passenger will need to wait between 15 minutes and 30 minutes?

c = 15 , d = 30

P(Between c and d ) = (d - c ) / ( b - a)

= (30 - 15) / ( 35 - 0)

= 15/35

= 0.429

Probability = 0.429

b)  What is the probability that a random passenger will need to wait more than 15 minutes?

P(More than 15 ) = (b - 15) / (b - a) = (35 - 15) / (35 - 0) = 20/35 = 0.571

Probability =  0.571

c) What is the probability that a random passenger will need to wait less than 18 minutes?

P(Less than 18) = (18 - a) / (b - a) = (18 - 0) / )(35 - 0) = 18/35 = 0.514

Probability =  0.514