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* = 8* t*.

(Round your answers to three decimal places.)

(a) What is the probability that exactly 7 small aircraft arrive during a 1-hour period?____________

What is the probability that at least 7 small aircraft arrive during a 1-hour period?_____________

What is the probability that at least 12 small aircraft arrive during a 1-hour period?_____________

(b) What is the expected value and standard deviation of the number of small aircraft that arrive during a 45-min period?

expected value____________

standard deviation_____________

(c) What is the probability that at least 26 small aircraft arrive during a 2.5-hour period?_____________

What is the probability that at most 11 small aircraft arrive during a 2.5-hour period?_____________

Answer #1

Please find the solution below:

The probability that exactly 7 small aircraft arrive during a 1-hour period = 0.6866.

The probability that at least 12 small aircraft arrive during a 1-hour period is 0.111924.

The Expected Vale is 6.

The Standard Deviation = 2.449.

The probability that at least 26 small aircraft arrive during a 2.5-hour period = 0.112185.

The probability that at most 11 small aircraft arrive during a 2.5-hour period =0.021387.

The probability that exactly 7 small aircraft arrive during a 1-hour period (with U = 8) is 0.139587.

End of the Solution...

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