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In: Statistics and Probability

Suppose small aircraft arrive at a certain airport according to a Poisson process with rate α...

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 6 small aircraft arrive during a 1-hour period?

What is the probability that at least 11 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 90-min period?

expected value    standard deviation    

(c)

What is the probability that at least 23 small aircraft arrive during a 2.5-hour period?

What is the probability that at most 15 small aircraft arrive during a 2.5-hour period?

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