
The cost per week on office repairs is normally distributed. If a random sample of repair bills is taken and the confidence interval is (95.25, 98.75), what is the error bound?

The error bound, also known as the margin of error, can be calculated from the confidence interval. Given the confidence interval \((95.25, 98.75)\), the error bound is the difference between the upper limit and the lower limit divided by 2.

Here's the step-by-step calculation:

1. **Identify the lower limit and upper limit of the confidence interval:**
   - Lower limit (\(L\)): 95.25
   - Upper limit (\(U\)): 98.75

2. **Calculate the margin of error (E):**
   \[
   E = \frac{U - L}{2}
   \]

Substituting the values:
\[
E = \frac{98.75 - 95.25}{2}
   = \frac{3.50}{2}
   = 1.75
\]

Therefore, the error bound is \(1.75\).

Would you like any additional details or explanations?

Here are 8 related questions:

1. What is the midpoint of the confidence interval given?
2. How would the error bound change if the confidence interval was wider?
3. How is the sample size related to the margin of error?
4. What assumptions are necessary for the confidence interval to be valid?
5. How would the margin of error be affected if the confidence level increased to 99%?
6. Can you explain the relationship between the standard deviation and the margin of error?
7. How would you interpret the error bound in the context of office repair costs?
8. What methods can be used to reduce the margin of error in future estimates?

**Tip:** Always ensure the confidence interval is properly calculated and interpreted, as this can significantly impact decision-making based on statistical data.

Learn how to calculate the error bound from a given confidence interval in statistics. Understand the margin of error concept and its application in data analysis. Suitable for undergraduate students studying statistics and data analysis.

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