4. Suppose small aircraft arrive at a certain airport, according to a Poisson pr

Question

4. Suppose small aircraft arrive at a certain airport, according to a Poisson process, at the rate of 6 per hour.

a. The probability that exactly 4 small aircraft arrive during a 1-hour period is i. 0.1339 ii. 0.8488 iii. 0.1339 iv. 2/3

b. The probability that at least 4 arrive during a 1-hour period is i. 0.1339 ii. 0.8488 iii. 0.1339 iv. 2/3
c. If we dene a working day as 12 hours, then the probability that at least 90 small aircraft arrive during a day is i. 0.9828 ii. 0.0225 iii. 0.0052 iv. 1/15

Explanation / Answer

Ans:

a)mean rate=6 per hr

P(x=4)=e-6*(6^4/4!)=0.1339

b)P(atleast 4)=P(x>=4)=1-P(x<=3)

=1-e-6*(60/0!+61/1!+62/2!+63/3!)

=1-e-6*(1+6+18+36)

=1-e-6*61=0.8488

c)Mean rate=12*6=72 per 12 hr

P(atleast 90)=P(x>=90)=1-P(x<=89)=1-poisson(89,72,true)

=0.0225

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