Determine the indicated probability for a Poisson random variable with the given values of $\lambda$ and t .
$\lambda = 0.8 , t = 8 , P ( 5 )$
A) 0.1468
B) 0.1487
C) 0.0005
D) 0.9995

Question

Determine the indicated probability for a Poisson random variable with the given values of $\lambda$ and  t .
$\lambda = 0.8 , t = 8 , P ( 5 )$
A)  0.1468 
B)  0.1487 
C)  0.0005 
D)  0.9995

Quizplus · Accepted Answer

The probability of observing exactly $k$ events in a Poisson distribution is given by the formula $P(k) = \frac{e^{-\lambda t}(\lambda t)^k}{k!}$. Here, $\lambda = 0.8$, $t = 8$, and $k = 5$. Plugging these values into the formula gives $P(5) = \frac{e^{-0.8*8}(0.8*8)^5}{5!}$, which calculates to approximately 0.1487.

Determine the Indicated Probability for a Poisson Random Variable with the Given