Question

Suppose small aircraft arrive at a certain airport according to a Poisson process with rate α = 8 per hour, so that the number of arrivals during a time period of t hours is a Poisson rv with parameter μ = 8t. (Round your answers to three decimal places.) (a) What is the probability that exactly 6 small aircraft arrive during a 1-hour period? What is the probability that at least 14 small aircraft arrive during a 1-hour period? What is the expected value and standard deviation of the number of small aircraft that arrive during a 75-min period? expected value standard deviation (b) (c) What is the probability that at least 25 small aircraft arrive during a 2.5-hour period? What is the probability that at most 18 small aircraft arrive during a 2.5-hour period?

Answer 1

a)

probability(exactly 6) =

P(X=6)=

{e-λ*λx/x!}=

0.122

probability(at least 6) =

P(X>=6)=

1-P(X<=5)=

1-∑x=0x-1   {e-λ*λx/x!}=

0.809

probability(at least 14) =

P(X>=14)=

1-P(X<=13)=

1-∑x=0x-1   {e-λ*λx/x!}=

0.034

b)expcted value =8*75/60=10

standard deviation =sqrt(10) =3.162

c)

probability (at least 25)=

P(X>=25)=

1-P(X<=24)=

1-∑x=0x-1   {e-λ*λx/x!}=

0.157

probability (at most 18)=

P(X<=18)=

∑x=0x   {e-λ*λx/x!}=

0.381