given that x has a poisson distribution with $\mu = 1.3$, what is the probability that $x = 3$?

$p(3) \approx$ (round to four decimal places as needed.)

Question

given that x has a poisson distribution with $\mu = 1.3$, what is the probability that $x = 3$?

$p(3) \approx$   (round to four decimal places as needed.)

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Poisson Distribution", "Poisson Probability Formula" ], "current_concepts": [ "Poisson Distribution", "Poisson Probability Formula" ] } ## State the Poisson probability formula $$ P(x) = \frac{e^{-\mu} \cdot \mu^x}{x!} $$ ## Substitute the given parameters $$ \begin{aligned} \mu &= 1.3 \ x &= 3 \ P(3) &= \frac{e^{-1.3} \cdot 1.3^3}{3!} \end{aligned} $$ ## Calculate the numerical value $$ \begin{aligned} e^{-1.3} &\approx 0.27253179 \ 1.3^3 &= 2.197 \ 3! &= 6 \ P(3) &\approx \frac{0.27253179 \cdot 2.197}{6} \approx 0.099791 \approx 0.0998 \end{aligned} $$ Given that x has a Poisson distribution with $\mu = 1.3$, what is the probability that $x = 3$? $P(3) \approx$ 0.0998 (Round to four decimal places as needed.) { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Statistics", "Poisson Distribution" ] }

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Question

Explanation:

State the Poisson probability formula

Substitute the given parameters

Calculate the numerical value

Answer: