Question

(3 markah/marks) Sebuah landasan di suatu lapangan terbang boleh menampung secara purata 120 pendaratan dan perlepasan kapal terbang untuk satu han Jadkan 2.7183 dan hitung perkara-perkara benikut A runway at an airport can handle an average of 120 flights arriving and departing per day. Lete 2.7183 and calculate the following (a) Cari kebarangkalian terdapat 2 atau kurang kapal terbang yang mendarat atau berlepas daripada landasan tersebut dalam tempoh satu jam Find the probability that there are 2 or fower flights arriving or departing from the runway in an hour (2 markah/marks) (b) Apakah jumlah kapal terbang yang dijangka mendarat dan berlepas dalam tempoh 4 jam? What is the expected number of flights arriving and departing in 4 hours? (1 markah/mark (c) Cari kebarangkalian bahawa jumlah yang dijangka tersebut (yang diperoleh sebelum ini) memang mendarat atau berlepas dalam tempoh 4 jam Find the probability that this expected number of lights (obtained previously) actually amive or depart in a given 4 hour period (2 markah/marks)

Answer 1

Poisson distribution:

Mean, $\lambda$ =120 per day =120/24 per hour =5 per hour

Formula: P(X=x) = e^-$\lambda$$\lambda$^x/x!

(a)

The probability of 2 or fewer flights arriving or departing in an hour is:

P(X$\leq$2) =P(X=0)+P(X=1)+P(X=2)

=e^-5 5⁰/0! + e^-5 5¹/1! + e^-5 5²/2! =0.12465

(b)

E(flights arriving and departing in 4 hours) =5 per hour*4 hours =20 flights. ​​​​​​

(c)

Required mean, $\lambda$ =20

P(X=20) =e^-20 20²⁰/20! =0.08884​​​​​​