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Chapter 4: Q. 4. 31 (page 270)

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

Expert verified

a. The average number of texts received per hour is250024≈104.167.

b.poissonpdf(104.167,100)=0.03663

c.1- poissoncdf(104.167,100)≈1−0.36505=0.63495

Step by step solution

01

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.

02

Explanation (part a)

the probability that there are exactly 100 arrivals and departures in one hour 250024≈104.167.

03

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)=poissonpdf(104.167,100)≈0.03663

04

Explanation (part c)

the probability that there are at most 100 arrivals and departures in one hour P(x>100)=1−P(x≤100)=1−poissoncdf(104.167,100)≈1−0.36505=0.63495

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