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The problem is asking which battery is more likely to last for 8 hours based on the standard deviations for Brand A (1.8 hours) and Brand B (1.7 hours). You're being asked to determine how many standard deviations (SDs) an 8-hour duration would be below the mean for both brands.

### Steps to solve:

1. **Calculate Z-scores (standard deviations below the mean):**
   - Z = (X - μ) / σ
   - Where:
     - \( X \) is the time (8 hours),
     - \( μ \) is the mean battery life for each brand,
     - \( σ \) is the standard deviation for each brand.

However, the mean battery lives of Brand A and Brand B aren't explicitly provided. This makes it unclear how to compute the Z-scores accurately, unless the mean values are assumed or inferred from other parts of the problem.

### Let's proceed as if:
- We need to calculate how far 8 hours is from the mean (in SD units) for both brands.

Would you like me to proceed with sample assumptions for the means, or do you have the means provided elsewhere in the problem?

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Also, here are five related questions to expand on the topic:

1. How is the Z-score used in determining probabilities for normal distributions?
2. Why is knowing the standard deviation important in understanding data variability?
3. How would increasing the sample size of battery tests affect the standard deviation and mean estimates?
4. Can Z-scores be used to compare different data sets with different units? Why or why not?
5. How would you interpret a Z-score of 0 in this context?

**Tip:** When calculating Z-scores, make sure to use the actual values for the mean and standard deviation to ensure accurate comparisons.

You are headed for 8 hours at the beach. Which battery (Brand A or Brand B) is more likely to last all day based on the standard deviations of 1.8 hours for Brand A and 1.7 hours for Brand B?

Determine which battery brand (Brand A or Brand B) is more likely to last for 8 hours at the beach. This problem involves calculating Z-scores based on given standard deviations for each brand, with Brand A at 1.8 hours and Brand B at 1.7 hours. A useful exercise in understanding Z-scores and standard deviations.

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