Island Airways flight 1580 offers daily service between Summerland and Chula Vis

Question

Island Airways flight 1580 offers daily service between Summerland and Chula Vista. Flight 1580 is scheduled to depart from Summerland Regional Airport at 8:00 A.M. However, the actual departure time is uniformly distributed between 8:00 A.M. and 9:00 A.M. You are a resident of Summerland, and this year you decide to go to Chula Vista for your summer vacation. Looking for the cheapest fare on the internet, you book yourself in Island Airways flight 1580. On the day of your trip, a big traffic jam delays your arrival at the airport. Because of the traffic jam and the long lines at the airport's security checkpoints, the time you will show up at the departure gate is uniformly distributed between 8:15 A.M. and 8:45 A.M. It is assumed that the departure of flight 1580 and your showing up at the gate arc independent events. (a) What is the probability that you will catch your flight? (b) You show up at the gate and your flight has not departed yet. What is the probability that your flight will leave within the next 5 minutes?

Explanation / Answer

let t=0 refers to time 8:00AM and t=60 refers to time 9:00 AM

from unifomr distribution P(X<x) =x/(60-0) =x/60

a) probabilty that you catch the flight =flight leaves after 8:15 AM =P(X>15)=1-P(X<15)=1-15/60=0.75

b)probabilty flight leaves with in 5 minute of your arrival =P(15<X<50) =(50-15)/60 =35/60=7/12=0.5833

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.