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.