Math Problem Statement
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?
Solution
To calculate the standard error of the mean (SEM), you can use the following formula:
where:
- is the sample standard deviation,
- is the sample size.
Given:
- minutes,
- .
Substitute these values into the formula:
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?
Here are 5 related questions to explore this topic further:
- How would the confidence interval change if the confidence level were 95% instead of 90%?
- What would happen to the SEM if the sample size increased to 100?
- How is the confidence interval calculated using the SEM and z-score?
- Why is the z-score chosen for the 90% confidence level in this problem?
- 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.
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Math Problem Analysis
Mathematical Concepts
Statistics
Confidence Intervals
Standard Error
Formulas
Standard Error of the Mean (SEM) = s / √n
Theorems
Central Limit Theorem
Suitable Grade Level
Grades 10-12
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