miles driven per day a random sample of 41 drivers found that they had driven on average 22 miles per day.

part 1 of 2

(a) find the 95% confidence interval of the mean for all drivers if the standard deviation of the population is 4.8. round your answers to one decimal place.

$\square

Question

miles driven per day a random sample of 41 drivers found that they had driven on average 22 miles per day.

part 1 of 2

(a) find the 95% confidence interval of the mean for all drivers if the standard deviation of the population is 4.8. round your answers to one decimal place.

$\square < \mu < \square$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Confidence Interval", "Z-Confidence Interval for Mean" ], "new_concepts": [], "current_concepts": [ "Confidence Interval", "Z-Confidence Interval for Mean" ] } ## Identify the given parameters $$ \begin{aligned} n &= 41 \ \bar{x} &= 22 \ \sigma &= 4.8 \ \text{Confidence Level} &= 95\% \implies z_{\alpha/2} = 1.96 \end{aligned} $$ ## Calculate the margin of error $$ \begin{aligned} E &= z_{\alpha/2} \cdot \frac{\sigma}{\sqrt{n}} \ E &= 1.96 \cdot \frac{4.8}{\sqrt{41}} \ E &\approx 1.96 \cdot 0.7496 \approx 1.469 \end{aligned} $$ ## Determine the confidence interval limits $$ \begin{aligned} \text{Lower Limit} &= \bar{x} - E = 22 - 1.469 = 20.531 \approx 20.5 \ \text{Upper Limit} &= \bar{x} + E = 22 + 1.469 = 23.469 \approx 23.5 \end{aligned} $$ 20.5 $< \mu <$ 23.5 { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Statistics", "Z-Confidence Interval for Mean" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the given parameters

Calculate the margin of error

Determine the confidence interval limits

Answer: