A delivery company provides expected time of arrival. The company wants to provide an accurate suggestion with a 90% confidence level. If the sample size is 50, the sample average is 35 minutes, the standard deviation is 10 minutes, and the z-score is 1.65, what is the standard error of the mean?

To calculate the standard error of the mean (SEM), you can use the following formula:

\[
\text{SEM} = \frac{s}{\sqrt{n}}
\]

where:
- \( s \) is the sample standard deviation,
- \( n \) is the sample size.

Given:
- \( s = 10 \) minutes,
- \( n = 50 \).

Substitute these values into the formula:

\[
\text{SEM} = \frac{10}{\sqrt{50}} = \frac{10}{7.071} \approx 1.414 \, \text{minutes}
\]

### Answer:
The standard error of the mean (SEM) is approximately **1.414 minutes**.

Would you like a detailed explanation of the steps or any clarification?

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Here are 5 related questions to explore this topic further:
1. How would the confidence interval change if the confidence level were 95% instead of 90%?
2. What would happen to the SEM if the sample size increased to 100?
3. How is the confidence interval calculated using the SEM and z-score?
4. Why is the z-score chosen for the 90% confidence level in this problem?
5. How does increasing the sample size affect the accuracy of the expected time of arrival?

**Tip:** The standard error decreases as sample size increases, making estimates more precise.

Learn how to calculate the standard error of the mean (SEM) for expected delivery time. This problem involves statistics concepts, including confidence intervals and standard deviation, using a sample size of 50, sample average of 35 minutes, and standard deviation of 10 minutes, at a 90% confidence level. Suitable for students in Grades 10-12.

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