The lifetime of a certain type of battery is known to be normally distributed with standard deviation o = 17 hours. A sample of 50 batteries had a mean lifetime
of 120.1 hours. It is desired to construct a 95% confidence interval for the mean lifetime for this type of battery. What is the standard error?

To calculate the **standard error (SE)** of the sample mean, use the formula:

\[
SE = \frac{\sigma}{\sqrt{n}}
\]

Where:
- \(\sigma = 17\) hours (the population standard deviation),
- \(n = 50\) (the sample size).

### Step-by-Step Calculation:
\[
SE = \frac{\sigma}{\sqrt{n}} = \frac{17}{\sqrt{50}}
\]

\[
\sqrt{50} \approx 7.071
\]

\[
SE \approx \frac{17}{7.071} \approx 2.404
\]

### Final Answer:
The standard error (SE) is approximately **2.404 hours**.

---

Would you like assistance calculating the confidence interval or more explanation? Here are 5 related questions to expand:

1. How is the confidence interval constructed for a population mean?
2. Why is the standard error important in statistical inference?
3. What is the z-score for a 95% confidence interval, and how is it applied?
4. How would the sample size affect the width of the confidence interval?
5. How does the assumption of normality influence this calculation?

**Tip:** For normally distributed data, knowing the standard deviation helps directly compute the standard error and confidence intervals effectively!

The lifetime of a certain type of battery is known to be normally distributed with standard deviation o = 17 hours. A sample of 50 batteries had a mean lifetime of 120.1 hours. It is desired to construct a 95% confidence interval for the mean lifetime for this type of battery. What is the standard error?

Learn how to calculate the standard error for a battery lifetime distribution. This problem involves statistical concepts such as standard deviation, sample size, and the formula SE = σ / √n. Suitable for Grades 10-12 students and anyone studying confidence intervals.

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