let $x$ be a binomial random variable with $n = 5$, $p = 0.3$. find the following value. (round your answer to three decimal places.)

$p(x = 4)$

Question

let $x$ be a binomial random variable with $n = 5$, $p = 0.3$. find the following value. (round your answer to three decimal places.)

$p(x = 4)$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Binomial Probability Distribution" ], "new_concepts": [], "current_concepts": [ "Binomial Probability Distribution" ] } ## Identify the given parameters Using the *Binomial Probability Distribution* knowledge point $$ \begin{aligned} &n = 5\ &p = 0.3\ &q = 1 - p = 0.7\ &k = 4 \end{aligned} $$ ## Apply the binomial formula Using the *Binomial Probability Distribution* knowledge point $$ \begin{aligned} P(x = k) &= \binom{n}{k} p^k q^{n-k}\ P(x = 4) &= \binom{5}{4} (0.3)^4 (0.7)^{5-4} \end{aligned} $$ ## Calculate the combination and powers Using the *Binomial Probability Distribution* knowledge point $$ \begin{aligned} \binom{5}{4} &= 5\ (0.3)^4 &= 0.0081\ (0.7)^1 &= 0.7 \end{aligned} $$ ## Compute the final probability Using the *Binomial Probability Distribution* knowledge point $$ \begin{aligned} P(x = 4) &= 5 \times 0.0081 \times 0.7\ P(x = 4) &= 0.02835\ P(x = 4) &\approx 0.028 \end{aligned} $$ Let $x$ be a binomial random variable with $n = 5$, $p = 0.3$. Find the following value. (Round your answer to three decimal places.) $P(x = 4) =$ 0.028 { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Statistics", "Binomial Probability Distribution" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the given parameters

Apply the binomial formula

Calculate the combination and powers

Compute the final probability

Answer: