If the covariance between x and y is 30. variance of A is 25 and variance of y is 144, then what is the correlation coefficient?

Options

A. 0.4
B. 0.5
C. 0.6
D. 0.7

Answer

To find the correlation coefficient between variables \( x \) and \( y \), we can use the formula:

\[ r_{xy} = \frac{\text{Cov}(x, y)}{\sqrt{\text{Var}(x) \cdot \text{Var}(y)}} \]

### Step-by-Step Solution:

1. **Identify the given values:**
- Covariance \( \text{Cov}(x, y) = 30 \)
- Variance of \( x \) \( \text{Var}(x) = 25 \)
- Variance of \( y \) \( \text{Var}(y) = 144 \)

2. **Substitute the values into the correlation formula:**
\[ r_{xy} = \frac{30}{\sqrt{25 \cdot 144}} \]

3. **Calculate the product of the variances:**
- \( 25 \cdot 144 = 3600 \)

4. **Calculate the square root of the product:**
\[ \sqrt{3600} = 60 \]

5. **Substitute back into the formula:**
\[ r_{xy} = \frac{30}{60} \]

6. **Simplify the fraction:**
\[ r_{xy} = \frac{1}{2} = 0.5 \]

### Final Answer:
The correlation coefficient \( r_{xy} \) is \( 0.5 \).