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 267 millimeters with a standard deviation of
39 mm. For pompano, the mean is 155 mm with a standard deviation of 28 mm.

Answer 1

Using the normal distribution, it is found that due to the greater z-score, Stewart caught the longer fish relative to the same specie.

Normal Probability Distribution

The z-score of a measure X of a normally distributed variable with mean $\mu$ and standard deviation $\sigma$ is given by:

$Z = \frac{X - \mu}{\sigma}$

• The z-score measures how many standard deviations the measure is above or below the mean.

• Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.

To find who caught the longer fish relative to the same specie, we need to find out who had the higher z-score.

Stewart caught a bluefish with a length of 322 mm, hence the parameters are as follows:

$X = 322, \mu = 267, \sigma = 39$

The z-score is:

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{322 - 267}{39}$

Z = 1.41

Gina caught a pompano with a length of 176 mm, hence the parameters are as follows:

$X = 176, \mu = 155, \sigma = 28$

The z-score is:

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{176 - 155}{28}$

Z = 0.75.

Hence Stewart caught the longer fish relative to the same specie.

More can be learned about the normal distribution at https://brainly.com/question/4079902

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