Answer-first summary for fast verification
Answer: $533,333
## Explanation The standard error of the sample mean is calculated using the formula: $$SE = \frac{\sigma}{\sqrt{n}}$$ Where: - $\sigma$ = population standard deviation = $3.2$ million - $n$ = sample size = 36 First, calculate the square root of the sample size: $$\sqrt{36} = 6$$ Then calculate the standard error: $$SE = \frac{3.2 \text{ million}}{6} = 0.533333 \text{ million}$$ Convert to dollars: $$0.533333 \text{ million} = \$533,333$$ **Why the other options are incorrect:** - **Option A ($88,889)**: This would be $3.2 \text{ million} ÷ 36$, which incorrectly divides by n instead of √n - **Option B ($400,000)**: This would be $3.2 \text{ million} ÷ 8$, which uses √64 instead of √36 The correct answer is **C. $533,333**.
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An analyst gathered the following information about a stock index:
| Mean net income for all companies in the index | $2.4 million |
|---|---|
| Standard deviation of net income for all companies in the index | $3.2 million |
If the analyst takes a sample of 36 companies from the index, the standard error of the sample mean is closest to:
A
$88,889
B
$400,000
C
$533,333
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