Question

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

Answer 1

Answer:

P=0.2613

Step-by-step explanation:

-Notice that this is a poison probability distribution problem.

-The Poisson probability function is expressed as:

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

where:

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

Given that x= 2 and $\lambda=2.4$, the probability is calculated as:

$P(X=2)=\frac{\lambda^xe^{-\lambda}}{x!}\\\\=\frac{2.4^2e^{-2.4}}{2!}\\\\\\=0.2613$

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