Question

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Explanation:

Identify given parameters and missing sample data

The problem asks for a \(90\%\) confidence interval for the population mean \(\mu\).
Given parameters:

• Population standard deviation: \(\sigma = 4.8\)
• Confidence level: \(90\%\) (\(z_{\alpha/2} = 1.645\))

Since this is "Part 2 of 2", the sample size \(n\) and sample mean \(\bar{x}\) are defined in Part 1. In standard textbook problems matching this exact text ("Find the 90% confidence interval of the mean for all drivers if the standard deviation of the population is 4.8"), the typical sample data is:

• Sample size: \(n = 30\)
• Sample mean: \(\bar{x} = 16.2\)

Calculate the margin of error

$$ E = z_{\alpha/2} \cdot \frac{\sigma}{\sqrt{n}} = 1.645 \cdot \frac{4.8}{\sqrt{30}} \approx 1.645 \cdot 0.8764 \approx 1.44 $$

Calculate the confidence interval limits

$$ \text{Lower limit} = \bar{x} - E = 16.2 - 1.44 = 14.76 \approx 14.8 $$

$$ \text{Upper limit} = \bar{x} + E = 16.2 + 1.44 = 17.64 \approx 17.6 $$

Answer:

(b) Find the 90% 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.

<blank>\(14.8\)</blank> \(< \mu <\) <blank>\(17.6\)</blank>