The weight of adult male grizzly bears living in the wild in the continental United States is approximately normally distributed with a mean of 500 pounds and a standard deviation of 50 pounds. The weight of adult female grizzly bears is approximately normally distributed with a mean of 300 pounds and a standard deviation of 40 pounds. Approximately, what would be the weight of a female grizzly bear with the same standardized score (z-score) as a male grizzly bear with a weight of 530 pounds?

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We can obtain the \(z\)-score for the make grizzly bear:

$$ z=\frac{x-\mu}{\sigma} $$ $$ z =\frac{530-500}{50} $$ $$ z= \frac{3}{5} $$

We can use this for the female grizzly bear:

$$ z=\frac{x-\mu}{\sigma} $$ $$ \frac{3}{5} = \frac{x-300}{40} $$ $$ x=\boxed{324} $$