Question

Gina and Stewart are surf-fishing on the Atlantic coast, where both bluefish and pompano are common catches. The mean length of a bluefish is 288 millimeters with a standard deviation of 51 mm. For pompano, the mean is 129 mm with a standard deviation of 40 mm. Stewart caught a bluefish that was 321 mm long. What was the z-score for this length?

Answer 1

Answer:

0.647

Step-by-step explanation:

The z-score of a variable, $x$, is given by

$z = \dfrac{x-\mu}{\sigma}$

where $\mu$ is the mean and $\sigma$ is the standard deviation.

For a bluefish, $\mu=288$ and $\sigma = 51$. The z-score for $x=321$ is

$z = \dfrac{321-288}{51}=\dfrac{33}{51} = 0.647$