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 9 small aircraft arrive during a 1-hour period?

Answer 1

Answer:

0.124 = 12.4% probability that exactly 9 small aircraft arrive during a 1-hour period.

Step-by-step explanation:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

$P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}$

In which

x is the number of sucesses

e = 2.71828 is the Euler number

$\mu$ is the mean in the given time interval.

Rate of 8 per hour

This means that $\mu = 8$

(a) What is the probability that exactly 9 small aircraft arrive during a 1-hour period?

This is P(X = 9).

$P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}$

$P(X = 9) = \frac{e^{-8}*8^{9}}{(9)!} = 0.124$

0.124 = 12.4% probability that exactly 9 small aircraft arrive during a 1-hour period.