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?_____________
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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