Question 1180571
Here's how to solve this problem:

**a. Range of expenditures for the lowest 10%:**

1.  **Find the z-score:** We're looking for the 10th percentile of the distribution. Use a z-table or calculator to find the z-score that corresponds to 0.10 (or 10%) of the area to the *left* of the mean. This z-score is approximately -1.28.

2.  **Convert to expenditure:** Use the z-score formula to convert this to a dollar amount:

    x = μ + zσ
    x = $5700 + (-1.28)($1500)
    x = $5700 - $1920
    x = $3780

So, the range of expenditures for the lowest 10% of families is from $0 to $3780.

**b. Percentage of families spending more than $7000:**

1.  **Calculate the z-score:**

    z = (x - μ) / σ
    z = ($7000 - $5700) / $1500
    z = $1300 / $1500
    z ≈ 0.87

2.  **Find the probability:** Use a z-table or calculator to find the area to the *right* of z = 0.87. This represents the percentage of families spending more than $7000.  P(z > 0.87) is approximately 0.1922 or 19.22%.

**c. Range of expenditures for the highest 5%:**

1.  **Find the z-score:** We're looking for the 95th percentile (since we want the top 5%). Use a z-table or calculator to find the z-score that corresponds to 0.95 (or 95%) of the area to the *left* of the mean. This z-score is approximately 1.645.

2.  **Convert to expenditure:**

    x = μ + zσ
    x = $5700 + (1.645)($1500)
    x = $5700 + $2467.50
    x = $8167.50

So, the range of expenditures for the highest 5% of families is from $8167.50 and above.

**Answers:**

*   a. The range of expenditures for the lowest 10% of families is from $0 to $3780.
*   b. Approximately 19.22% of families spend more than $7000 annually on food and drink.
*   c. The range of expenditures for the highest 5% of families is from $8167.50 and above.