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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?

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adelekeademolu

Answer:

0.647

Step-by-step explanation:

The z-score of a variable, [tex]x[/tex], is given by

[tex]z = \dfrac{x-\mu}{\sigma}[/tex]

where [tex]\mu[/tex] is the mean and [tex]\sigma[/tex] is the standard deviation.

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

[tex]z = \dfrac{321-288}{51}=\dfrac{33}{51} = 0.647[/tex]

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