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 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...