If the standard deviation of x is 18,the covariance of x and y is 120,the coefficient r = 0.90,then the standard deviation of y is 54.87.

Question

Quizplus · Accepted Answer

Given that the coefficient of correlation $r = 0.90$, the covariance of $x$ and $y$ is $120$, and the standard deviation of $x$ is $18$, we can find the standard deviation of $y$ ($\sigma_y$) using the formula for the correlation coefficient $r = \frac{cov(x, y)}{\sigma_x \sigma_y}$. Rearranging this formula to solve for $\sigma_y$ gives $\sigma_y = \frac{cov(x, y)}{r \cdot \sigma_x}$. Plugging in the given values, $\sigma_y = \frac{120}{0.90 \cdot 18} = \frac{120}{16.2} = 7.41$, not $54.87$.

If the Standard Deviation of X Is 18,the Covariance of X