The given formula is:

$E = z^* \left( \frac{\sigma}{\sqrt{n}} \right)$

Where:

• $z^* = 2.576$
• $\sigma = 32.39$
• $n = 50$

Now, let's calculate $E$.

1. First, find the standard error of the mean ($\frac{\sigma}{\sqrt{n}}$):

$\frac{\sigma}{\sqrt{n}} = \frac{32.39}{\sqrt{50}} = \frac{32.39}{7.071} \approx 4.58$

2. Next, multiply $z^*$ by the standard error:

$E = 2.576 \times 4.58 \approx 11.81$

Thus, the value of $E$ is approximately 11.810 (rounded to three decimal places).

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Would you like further explanation on how to interpret or use this result? Here are some follow-up questions:

1. What is the interpretation of $E$ in this formula?
2. How does the sample size $n$ affect the value of $E$?
3. What is the significance of $z^* = 2.576$?
4. How can this formula be applied in hypothesis testing?
5. What happens to $E$ if the standard deviation $\sigma$ is increased?

Tip: When rounding intermediate steps, it's best to carry out calculations with full precision to avoid small rounding errors affecting the final answer.