77% of u.s. adults think that political correctness is a problem in america today. you randomly select six u.s. adults and ask them whether they think that political correctness is a problem in america today. the random variable represents the number of u.s. adults who think that political correctness is a problem in america today. answer the questions below.

find the mean of the binomial distribution.
$\mu = 4.6$ (round to the nearest tenth as needed.)

find the variance of the binomial distribution.
$\sigma^2 = 1.1$ (round to the nearest tenth as needed.)

find the standard deviation of the binomial distribution.
$\sigma = 1.0$ (round to the nearest tenth as needed.)

interpret the standard deviation in the context of the real-life situation.

most samples of 6 adults would differ from the mean by no more than values further from the mean than that would be considered unusual.
(type integers or decimals rounded to the nearest tenth as needed.)

Question

77% of u.s. adults think that political correctness is a problem in america today. you randomly select six u.s. adults and ask them whether they think that political correctness is a problem in america today. the random variable represents the number of u.s. adults who think that political correctness is a problem in america today. answer the questions below.

find the mean of the binomial distribution.
$\mu = 4.6$ (round to the nearest tenth as needed.)

find the variance of the binomial distribution.
$\sigma^2 = 1.1$ (round to the nearest tenth as needed.)

find the standard deviation of the binomial distribution.
$\sigma = 1.0$ (round to the nearest tenth as needed.)

interpret the standard deviation in the context of the real-life situation.

most samples of 6 adults would differ from the mean by no more than   values further from the mean than that would be considered unusual.
(type integers or decimals rounded to the nearest tenth 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": [ "Binomial Distribution Mean", "Binomial Distribution Variance", "Binomial Distribution Standard Deviation" ], "new_concepts": [], "current_concepts": [ "Binomial Distribution Mean", "Binomial Distribution Variance", "Binomial Distribution Standard Deviation", "Standard Deviation Interpretation" ] } ## Identify binomial parameters $$ \begin{aligned} n &= 6 \ p &= 0.77 \ q &= 1 - p = 0.23 \end{aligned} $$ ## Calculate standard deviation $$ \begin{aligned} \mu &= n \cdot p = 6 \cdot 0.77 = 4.62 \approx 4.6 \ \sigma^2 &= n \cdot p \cdot q = 6 \cdot 0.77 \cdot 0.23 = 1.0626 \approx 1.1 \ \sigma &= \sqrt{1.0626} \approx 1.0308 \approx 1.0 \end{aligned} $$ ## Interpret standard deviation $$ \text{Standard deviation value} = 1.0 $$ Most samples of 6 adults would differ from the mean by no more than 1.0. Values further from the mean than that would be considered unusual. { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Statistics", "Binomial Distribution Standard Deviation" ] }

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Question

Explanation:

Identify binomial parameters

Calculate standard deviation

Interpret standard deviation

Answer: