Question

Atlanta’s Hartsfield-Jackson International Airport is the busiest airport in the world. On average there are $2,500$arrivals and departures each day.

a. How many airplanes arrive and depart the airport per hour?

b. What is the probability that there are exactly $100$arrivals and departures in one hour?

c. What is the probability that there are at most $100$arrivals and departures in one hour?

Short answer

(a) Every hour, flights arrive and depart from the airport is$104.1667$

(b) Probability for exactly $100$departure and arrivals $P(X=100)=0.0366$

(c) Probability for most $100$departure and arrivals$P(X\le 100)=0.365$

Step-by-step solution

Find Every hour, flights arrive and depart from the airport (part a)

In a single day, there are $2500$arrivals and departures.

Let $X$indicate the total number of arrivals and departures in one hour.

In one hour, the overall amount of arrivals and departures is

$\frac{1}{24}2500=104.1667$

Find probability (part b)

With a mean of $104.1667$variable $X$has a Poisson distribution. There's a good chance there will be $100$arrivals and departs.

$P(X=100)=0.0366$

Find probability (part c)

There's a good chance there will be no more than 100 arrivals and departures.

$P(X\le 100)=0.365$