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katen-ka-za
1 month ago
6

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]1 month ago
3 0

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.

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