The following data represent a sample of the assets (in millions of dollars) of
28
credit unions in a state. Assume that the population in this state is normally distributed with
σ
=
3.5
million dollars. Use Excel to find the
99
%
confidence interval of the mean assets in millions of dollars. Round your answers to three decimal places and use ascending order.

Assets
12.23
2.89
13.19
73.25
11.59
8.74
7.92
40.22
5.01
2.27
16.56
1.24
9.16
1.91
6.69
3.17
4.78
2.42
1.47
12.77
4.39
2.17
1.42
14.64
1.06
18.13
16.85
21.58

To calculate the 99% confidence interval for the mean of the assets using Excel, you can follow these steps:

### Step 1: Input the Data
1. Enter the given data into a column in Excel. For example, enter the data from cell A1 to A28.

### Step 2: Calculate the Mean
1. Use the `AVERAGE` function to calculate the mean (x̄) of the data.
   - Formula: `=AVERAGE(A1:A28)`

### Step 3: Identify the Population Standard Deviation (σ)
1. The problem states that the population standard deviation (σ) is \(3.5\) million dollars.

### Step 4: Determine the Sample Size (n)
1. The sample size (n) is 28 (as there are 28 assets).

### Step 5: Find the Z-Score for the 99% Confidence Level
1. Use the `NORM.S.INV` function to find the Z-score corresponding to a 99% confidence level.
   - Formula: `=NORM.S.INV(0.995)`
   - The result is approximately \(2.576\).

### Step 6: Calculate the Margin of Error (E)
1. Use the formula \(E = Z \times \frac{\sigma}{\sqrt{n}}\) to calculate the margin of error.
   - Formula: `=2.576 * (3.5 / SQRT(28))`

### Step 7: Determine the Confidence Interval
1. Calculate the lower bound of the confidence interval:
   - Formula: `=Mean - E`
2. Calculate the upper bound of the confidence interval:
   - Formula: `=Mean + E`

### Example Calculation in Excel:
Assuming the data is in cells A1 to A28:

1. **Mean (x̄)**: `=AVERAGE(A1:A28)`
2. **Z-score for 99% Confidence Level**: `=NORM.S.INV(0.995)` (which gives approximately 2.576)
3. **Margin of Error (E)**: `=2.576 * (3.5 / SQRT(28))`
4. **Lower Bound**: `=Mean - E`
5. **Upper Bound**: `=Mean + E`

### Final Calculation:
Here’s how it would work with the exact numbers:

1. **Mean (x̄)**: Calculated using `=AVERAGE(A1:A28)`
2. **E**: Calculated using `=2.576 * (3.5 / SQRT(28))`
3. **Lower Bound**: `=Mean - E`
4. **Upper Bound**: `=Mean + E`

Let's calculate this:

1. **Mean**: \( \text{Mean} \approx 11.29 \)
2. **E**: \( \text{E} \approx 1.705 \)

Finally, the 99% confidence interval is:
\[ (11.29 - 1.705, 11.29 + 1.705) \]

So, the 99% confidence interval for the mean is approximately:
\[ (9.585, 12.995) \]

### Summary:
The 99% confidence interval for the mean assets is \(\textbf{(9.585, 12.995)}\) million dollars.

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Would you like a detailed explanation of any of these steps or help with further questions?

Here are five additional questions you might find interesting:

1. How would the confidence interval change if the sample size were increased to 50?
2. What would be the 95% confidence interval using the same data?
3. How does the confidence interval change if the standard deviation was unknown and estimated from the sample?
4. Can you determine the required sample size to achieve a margin of error of 1 million dollars with 99% confidence?
5. What is the effect of increasing the confidence level to 99.9%?

**Tip:** When calculating confidence intervals, remember that a higher confidence level results in a wider interval.

Learn how to calculate the 99% confidence interval for the mean assets using Excel. This problem involves applying statistical concepts such as Z-score, margin of error, and confidence intervals in a real-world scenario with financial data.

Math Problem Statement

The following data represent a sample of the assets (in millions of dollars) of 28 credit unions in a state. Assume that the population in this state is normally distributed with σ

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