Determine the indicated probability for a Poisson random variable with the given values of $\lambda$ and t .
$\lambda = 0.8 , t = 9 , P ( \text { More than } 3 )$
A) 0.0255
B) 0.9281
C) 0.0712
D) 0.0719

Question

Determine the indicated probability for a Poisson random variable with the given values of $\lambda$ and  t .
$\lambda = 0.8 , t = 9 , P ( \text { More than } 3 )$
A)  0.0255 
B)  0.9281 
C)  0.0712 
D)  0.0719

Quizplus · Accepted Answer

The probability of a Poisson random variable being more than a certain value is found by subtracting the cumulative probability of it being less than or equal to that value from 1. For $\lambda = 0.8$ and $t = 9$, the rate $\lambda t = 0.8 \times 9 = 7.2$. The probability of getting more than 3 occurrences is $1 - P(X \leq 3)$. Using a Poisson probability table or calculator for $P(X \leq 3)$ with $\lambda t = 7.2$, and then subtracting from 1, gives a value close to 0.9281, indicating that the probability of having more than 3 occurrences in this scenario is high.

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