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### Problem 2: Z-Scores Calculation for Vacation Expenses
You are given:
- Mean ($\mu$) = \$247 per day
- Standard deviation ($\sigma$) = \$60 per day

The z-score formula is:

\[
z = \frac{x - \mu}{\sigma}
\]

We need to find the z-scores for different vacation expenses:

a. **\$197 per day:**

\[
z = \frac{197 - 247}{60} = \frac{-50}{60} = -0.83
\]

b. **\$277 per day:**

\[
z = \frac{277 - 247}{60} = \frac{30}{60} = 0.50
\]

c. **\$310 per day:**

\[
z = \frac{310 - 247}{60} = \frac{63}{60} = 1.05
\]

### Problem 3: Z-Score Interpretation
A family had a z-score of 1.5. To find the daily expense for this family, we use the z-score formula in reverse:

\[
x = \mu + z \cdot \sigma
\]

Substitute the values:

\[
x = 247 + 1.5 \times 60 = 247 + 90 = 337
\]

So, the family spent **\$337 per day**.

### Problem 4: Percentage of Families' Spending Range
This problem requires understanding the percentages corresponding to z-scores in a normal distribution. The image mentions finding the percentages for different ranges of expenses, but we need z-scores to answer that correctly. I'll need a bit more detail on the z-scores or exact instructions to fully answer.

Would you like more details on solving this problem with z-scores?

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**Follow-up questions**:
1. What is the general formula for calculating a z-score?
2. How does changing the standard deviation affect the spread of data?
3. How would you calculate the percentage of families spending less than \$167?
4. What does a z-score of 0 represent in this context?
5. Can you explain how z-scores relate to real-life situations, such as this vacation expense scenario?

**Tip**: Understanding the z-score formula and its use in normal distributions is key for interpreting how data points compare to the mean in standardized terms.

A survey by the American Automobile Association shows that the average vacation expense for food and lodging in the US is $247 per day, with a standard deviation of $60. The problem involves calculating z-scores for different expenses and interpreting the results, as well as answering questions related to vacation expenses.

Learn how to calculate z-scores and interpret their significance in the context of vacation expenses. This problem explores key statistical concepts such as the normal distribution and standard deviation, with detailed step-by-step solutions for calculating z-scores. Suitable for students in Grades 9-12.

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