Questions: definitely not related. definitely positively related. probably negatively related. definitely related. probably not related. definitely negatively related. probably positively related. probably related.

Solution Steps

The covariance between the letter counts in first names \( X \) and last names \( Y \) is calculated as follows:

\[ \text{Cov}(X,Y) = 3.0 \]

The standard deviations for the letter counts in first names and last names are given by:

\[ \sigma_X = 1.58 \] \[ \sigma_Y = 2.07 \]

The correlation coefficient \( r \) is calculated using the formula:

\[ r = \frac{\text{Cov}(X,Y)}{\sigma_X \sigma_Y} \]

Substituting the values:

\[ r = \frac{3.0}{1.58 \times 2.07} \approx 0.91 \]

Final Answer