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a statistics professor finds that when she schedules an office hour for student help, an average of 2.4 students arrive. find the probability that in a randomly selected office hour, the number of student arrivals is 2

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opudodennis

Answer:

P=0.2613

Step-by-step explanation:

-Notice that this is a poison probability distribution problem.

-The Poisson probability function is expressed as:

[tex]P(X=x)=\frac{\lambda^x e^{-\lambda}}{x!}[/tex]

where:

  • x=0,1,2,3
  • [tex]e[/tex] Euler's constant
  • [tex]\lambda[/tex] =mean number of occurrences.

Given that x= 2 and [tex]\lambda=2.4[/tex], the probability is calculated as:

[tex]P(X=2)=\frac{\lambda^xe^{-\lambda}}{x!}\\\\=\frac{2.4^2e^{-2.4}}{2!}\\\\\\=0.2613[/tex]

Hence, the  probability that in a randomly selected office hour, the number of student arrivals is 2 is 0.2613

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