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. The average number of texts received per hour is$\frac{2500}{24}\approx 104.167.$

b.$\text{poissonpdf}(104.167,100)=0.03663$

c.$1\text{- poissoncdf}(104.167,100)\approx 1-0.36505=0.63495$

Step-by-step solution

Given information

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

Explanation (part a)

the probability that there are exactly 100 arrivals and departures in one hour $\frac{2500}{24}\approx 104.167.$

Explanation (part  b)

the probability that a text message user receives or sends two messages per hour $X~P(104.167)$, so

$P(x=100)=\text{poissonpdf}(104.167,100)\approx 0.03663$

Explanation (part c)

the probability that there are at most 100 arrivals and departures in one hour $P(x>100)=1-P(x\le 100)=1-\text{poissoncdf}(104.167,100)\approx 1-0.36505=0.63495$