https://file.aiquickdraw.com/mathbot/file/17254207295180rni6cib.jpg

To solve the problem, we need to use the given formula:

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

Given values:
- \( z = 7.3 \)
- \( \mu = 6.9 \)
- \( \sigma = 7.2 \)
- \( n = 30 \)

We need to find \( x \) and round the answer to 4 decimal places.

### Step 1: Substitute the given values into the formula
\[
7.3 = \frac{x - 6.9}{\frac{7.2}{\sqrt{30}}}
\]

### Step 2: Calculate \(\frac{7.2}{\sqrt{30}}\)
\[
\frac{7.2}{\sqrt{30}} \approx \frac{7.2}{5.4772} \approx 1.3140
\]

### Step 3: Multiply both sides of the equation by 1.3140 to solve for \( x - \mu \)
\[
7.3 \times 1.3140 \approx 9.5922
\]
\[
x - 6.9 = 9.5922
\]

### Step 4: Solve for \( x \)
\[
x = 9.5922 + 6.9 = 16.4922
\]

### Final Answer
\[
x \approx 16.4922 \, (\text{rounded to 4 decimal places})
\]

Would you like further details on this solution, or do you have any questions?

Here are 5 related questions to further your understanding:
1. How would the result change if the sample size \( n \) was larger?
2. What is the significance of the z-score in this context?
3. How does changing \( \mu \) affect the value of \( x \)?
4. What assumptions are made about the distribution of the data when using this formula?
5. How would the solution differ if \( \sigma \) was different?

**Tip:** When solving for \( x \) using the z-score formula, make sure to isolate \( x \) properly by carefully performing each algebraic step.

Use the formula z = (x - μ) / (σ / √n) to find x when z = 7.3, μ = 6.9, σ = 7.2, and n = 30. Round to 4 decimal places.

Learn how to find x using the z-score formula when z = 7.3, μ = 6.9, σ = 7.2, and n = 30. This problem involves key concepts in statistics and algebra, ideal for students in Grades 10-12. The solution is rounded to four decimal places.

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