Question

Airplanes arrive at a regional airport approximately once every 15 minutes. If the probability of arrivals is exponentially distributed, the probability that a plane will arrive in less than 5 minutes is equal to 0.3333.

Answer 1

The answer is 0.2835

Given: Airplane arrives once every 15 minutes,

So Expected duration (µ) = 15

The rate parameter (λ) = 1/µ = 1/15

What is the expected duration (µ)?

Expected duration is the duration between two events to occur.

What is the rate parameter in exponential distribution?

The rate parameter shows how quickly the decay of the exponential function occurs. It is given by the reciprocal of expected duration that is λ = 1/µ,

where λ is the rate parameter and µ is the expected duration.

Also given that the probability of arrivals is exponentially distributed.

How to find the probability for some value (x) less than for some Random variable (X) that is distributed exponentially?

The probability for some value (x) less than for some Random variable (X) is given by

P(X<x) = 1- e^(-λx),

where

X = Random variable

x = value of some given specified condition

λ = rate parameter.

In the question, "a plane arrives in less than 5 minutes" so x = 5.

Therefore,

P(X<5) = 1 - e^(-1/15.5)

= 1 – 0.716531

= 0.283469 ≈ 0.2835.

Hence, the probability that a plane arrives in less than 5 minutes is 0.2835

Learn more about "exponential probability distribution" here: brainly.com/question/22985880

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