Suppose that the number of drivers who travel between a particular origin and destination during a designated time period has a

Question

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Suppose that the number of drivers who travel between a particular origin and destination during a designated time period has a

Poisson distribution with parameter μ = 20 (suggested in the article "Dynamic Ride Sharing: Theory and Practice"†). (Round your answer to three decimal places.) (a) What is the probability that the number of drivers will be at most 18?

Mathematics

1 answer:

AnnZ [12.3K] · Answer 1 · 2026-02-28T03:07:42+03:00

Answer:

The likelihood that the number of drivers is at most 18 is 0.381.

Step-by-step explanation:

We are provided with the following details in the question:

The quantity of drivers traveling between a specific origin and destination in a set time frame follows a Poisson distribution characterized by the parameter μ = 20.

The Poisson distribution defines the probability of a certain number of events taking place over a specific period, based on the mean frequency of those events.
The variance for the Poisson distribution matches its mean value of Poisson distribution.

a) P(number of drivers will be at most 18)

Equation:

$P(X =k) = \displaystyle\frac{\mu^k e^{-\mu}}{k!}\\\\ \mu \text{ is the mean of the distribution}$

$P( x \leq 18) =P(x=0) + P(x =1) + P(x = 2) +... + P(x = 18)\\\\= \displaystyle\frac{20^0 e^{-20}}{0!} + \displaystyle\frac{20^1 e^{-20}}{1!} +...+ \displaystyle\frac{20^{18} e^{-20}}{18!}\\\\ = 0.381$

So, 0.381 represents the probability that the number of drivers will be at most 18.