Question

The taxiways and runways of a major airport are carefully monitored to expedite takeoffs and landings and to prevent collisions. If a pedestrian or vehicle enters a radiocontrolled surface at an airport without receiving permission, this is called a deviation and incursion. Suppose the mean number of deviations and incursions per year at the Los Angeles International Airport (LAX) is 2. Find the probability that exactly 3 serious deviations and incursions will occur at LAX in a randomly selected year

Answer 1

Answer:

18.04% probability that exactly 3 serious deviations and incursions will occur at LAX in a randomly selected year

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.

Suppose the mean number of deviations and incursions per year at the Los Angeles International Airport (LAX) is 2.

This means that $\mu = 2$

Find the probability that exactly 3 serious deviations and incursions will occur at LAX in a randomly selected year

This is P(X = 3).

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

$P(X = 3) = \frac{e^{-2}*2^{3}}{(3)!} = 0.1804$

18.04% probability that exactly 3 serious deviations and incursions will occur at LAX in a randomly selected year