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The expression you have provided appears to be a statistical formula, likely for calculating a confidence interval for a proportion. It looks like this:

\[
0.36 + 1.960 \times \sqrt{\frac{0.36(1 - 0.36)}{56}}
\]

Let's break it down:

1. **0.36**: This appears to be the sample proportion (\( \hat{p} \)).
2. **1.960**: This is the critical value for a 95% confidence level (from the standard normal distribution, \( z \)-value).
3. **\( \sqrt{\frac{0.36(1 - 0.36)}{56}} \)**: This is the standard error of the proportion.

To solve it, we follow these steps:

### Step 1: Calculate \( 1 - 0.36 \)
\[
1 - 0.36 = 0.64
\]

### Step 2: Compute the standard error term inside the square root
\[
\frac{0.36 \times 0.64}{56} = \frac{0.2304}{56} = 0.00411429
\]

### Step 3: Take the square root
\[
\sqrt{0.00411429} \approx 0.06415
\]

### Step 4: Multiply by the critical value (1.960)
\[
1.960 \times 0.06415 \approx 0.125734
\]

### Step 5: Add this to the sample proportion
\[
0.36 + 0.125734 = 0.485734
\]

So, the result of the expression is approximately **0.486**.

Would you like a more detailed explanation of confidence intervals or any further calculations? 

### 5 Related Questions:
1. What does a confidence interval represent in statistics?
2. How is the critical value of 1.960 determined for a 95% confidence level?
3. What other methods can be used to calculate confidence intervals?
4. How does sample size affect the width of a confidence interval?
5. What assumptions are made when using this type of formula for proportions?

### Tip:
When calculating confidence intervals, always ensure your sample size is large enough to justify using normal approximations. For small samples, alternative methods such as exact confidence intervals may be more appropriate.

Calculate the confidence interval for the proportion 0.36 with a sample size of 56. The solution applies statistical methods such as the normal approximation and the formula for standard error of a proportion, including key calculations using the critical value of 1.960.

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