Questions: Luis caught a two-year-old flounder that was 185 millimeters in length. What is the z-score for this length? Round the answers to at least two decimal places. Luis's z-score is.

Solution Steps

To find the $z$-score for the length of the flounder, we need to know the mean and standard deviation of the lengths of two-year-old flounders. The $z$-score is calculated using the formula:

\[ z = \frac{(X - \mu)}{\sigma} \]

where \( X \) is the observed value (185 mm in this case), \( \mu \) is the mean, and \( \sigma \) is the standard deviation. Once we have the mean and standard deviation, we can plug these values into the formula to compute the $z$-score.

We are given the following values:

• Observed value \( X = 185 \) mm
• Mean \( \mu = 170 \) mm
• Standard deviation \( \sigma = 10 \) mm

The formula for calculating the \( z \)-score is:

\[ z = \frac{(X - \mu)}{\sigma} \]

Substituting the given values into the formula:

\[ z = \frac{(185 - 170)}{10} = \frac{15}{10} = 1.5 \]

The calculated \( z \)-score is already at two decimal places, so no further rounding is necessary. The \( z \)-score is \( 1.5 \).

Final Answer