let x be a binomial random variable with $n = 6$, $p = 0.3$. find the following value. (round your answer to three decimal places.)

\\sigma = \sqrt{npq}\

Question

let x be a binomial random variable with $n = 6$, $p = 0.3$. find the following value. (round your answer to three decimal places.)

\\sigma = \sqrt{npq}\

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", "Standard Deviation of Discrete Random Variable" ] } ## Identify the given parameters Using the *Binomial Probability Distribution* knowledge point $$ \begin{aligned} n &= 6 \ p &= 0.3 \end{aligned} $$ ## Calculate the probability of failure Using the *Binomial Probability Distribution* knowledge point $$ q = 1 - p = 1 - 0.3 = 0.7 $$ ## Calculate the standard deviation Using the *Binomial Probability Distribution* knowledge point $$ \begin{aligned} \sigma &= \sqrt{n p q} \ \sigma &= \sqrt{6 \times 0.3 \times 0.7} \ \sigma &= \sqrt{1.26} \end{aligned} $$ ## Round to three decimal places Using the *Binomial Probability Distribution* knowledge point $$ \begin{aligned} \sqrt{1.26} &\approx 1.122497... \ \sigma &\approx 1.122 \end{aligned} $$ Let $x$ be a binomial random variable with $n = 6$, $p = 0.3$. Find the following value. (Round your answer to three decimal places.) $\sigma = \sqrt{npq}$ 1.122 { "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

Calculate the probability of failure

Calculate the standard deviation

Round to three decimal places

Answer: