Use the Poisson Distribution to find the indicated probability. Round to three decimal places when necessary.
-$$\lambda = 3.1 ; \mathrm { P } ( \mathrm { X } \geq 2 )$$
A)$0.599$
B) $0.185$
C) $0.216$
D) $0.815$

Question

Use the Poisson Distribution to find the indicated probability. Round to three decimal places when necessary.
-$$\lambda = 3.1 ; \mathrm { P } ( \mathrm { X } \geq 2 )$$  
A)$0.599$
B) $0.185$
C) $0.216$
D) $0.815$

Quizplus · Accepted Answer

The probability that X is at least 2 is the complement of the probability that X is less than 2 (i.e., P(X=0) + P(X=1)). Using the Poisson formula, calculate P(X=0) and P(X=1), then subtract their sum from 1 to find P(X≥2). Calculation: P(X=0) = e^(-3.1)(3.1)^0/0! ≈ 0.045, P(X=1) = e^(-3.1)(3.1)^1/1! ≈ 0.140. Thus, P(X≥2) = 1 - (P(X=0) + P(X=1)) ≈ 1 - (0.045 + 0.140) = 0.815.

Use the Poisson Distribution to Find the Indicated Probability λ=3.1;P(X≥2)\lambda = 3.1 ; \mathrm { P } ( \mathrm { X } \geq 2 )λ=3.1;P(X≥2)

Use the Poisson Distribution to Find the Indicated Probability $\lambda = 3.1 ; \mathrm { P } ( \mathrm { X } \geq 2 )$