The combined city/highway fuel economy of a 2023 Lexus UX 250 Hybrid is a normally distributed random variable with a mean of μ = 26.75 mpg and a standard deviation of σ = 3.50 mpg. Within what interval would you expect the sample mean to fall, with 99 percent probability? Note: Round your answers to 4 decimal places.

To determine the interval within which the sample mean of the fuel economy would fall with 99 percent probability, we use the concept of the confidence interval for the sample mean.

Given:
- Mean (μ) = 26.75 mpg
- Standard deviation (σ) = 3.50 mpg
- Confidence level = 99%
- Sample size (n) = unknown (we assume the problem is asking for the interval of a single observation, meaning n=1)

For a 99% confidence level, the corresponding z-score from the standard normal distribution is approximately 2.576.

The formula for the confidence interval is:

\[
\text{Confidence Interval} = \mu \pm (z \cdot \frac{\sigma}{\sqrt{n}})
\]

Since we assume this is about a single observation, \( n = 1 \), so the formula simplifies to:

\[
\text{Confidence Interval} = 26.75 \pm (2.576 \cdot 3.50)
\]

Let's calculate this interval.The 99% confidence interval for the sample mean of the fuel economy is approximately \([17.7340, 35.7660]\) mpg.

This interval suggests that with 99 percent probability, the sample mean fuel economy for the 2023 Lexus UX 250 Hybrid will fall within this range.

Would you like further details, or do you have any questions?

Here are 5 related questions you might find interesting:
1. How does the confidence interval change if the sample size increases?
2. What would the confidence interval be with a 95% confidence level?
3. How do you interpret the meaning of the confidence interval in practical terms?
4. What is the impact of a larger standard deviation on the width of the confidence interval?
5. How would the interval change if we had more precise data with a smaller standard deviation?

**Tip:** The width of a confidence interval decreases as the sample size increases or the confidence level decreases.

Learn how to calculate the confidence interval for the sample mean of a 2023 Lexus UX 250 Hybrid's fuel economy, based on a normally distributed random variable with mean μ = 26.75 mpg and standard deviation σ = 3.50 mpg. With a 99% confidence level, explore the range within which the sample mean is expected to fall. Includes step-by-step solution and relevant statistical concepts.

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