nine plants are operated by a garment manufacturer. they feel there is a eighteen percent chance for a strike at any one plant and the risk of a strike at one plant is independent of the risk of a strike at another plant. let $x$ be the number of plants of the garment manufacturer that strike.

step 3 of 3: compute the standard deviation for $x$. round your answer to three decimal places, if necessary.

Question

nine plants are operated by a garment manufacturer. they feel there is a eighteen percent chance for a strike at any one plant and the risk of a strike at one plant is independent of the risk of a strike at another plant. let \$x\$ be the number of plants of the garment manufacturer that strike.

step 3 of 3: compute the standard deviation for \$x\$. round your answer to three decimal places, if necessary.

step 3 of 3: compute the standard deviation for $x$. round your answer to three decimal places, if necessary.

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 Distribution" ], "new_concepts": [ "Binomial Standard Deviation" ], "current_concepts": [ "Binomial Distribution", "Binomial Standard Deviation" ] } ## Identify binomial parameters Using the *Binomial Distribution* knowledge point $$ \begin{aligned} n &= 9 \ p &= 0.18 \ q &= 1 - p = 0.82 \end{aligned} $$ ## Calculate standard deviation $$ \begin{aligned} \sigma &= \sqrt{n \cdot p \cdot q} \ \sigma &= \sqrt{9 \cdot 0.18 \cdot 0.82} \ \sigma &= \sqrt{1.3284} \ \sigma &\approx 1.15256 \end{aligned} $$ ## Round to three decimal places $$ \sigma \approx 1.153 $$ Compute the standard deviation for $X$. Round your answer to three decimal places, if necessary. 1.153 { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Statistics", "Binomial Standard Deviation" ] }

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Question

Explanation:

Identify binomial parameters

Calculate standard deviation

Round to three decimal places

Answer: