Question

the lengths of mature trout in a local lake are approximately normally distributed with a mean of \\( \mu = 12.5 \\) inches, and a standard deviation of \\( \sigma = 1.7 \\) inches.
fill in the indicated boxes.
find the z - score corresponding to a fish that is 13.7 inches long. round your answer to the nearest hundredth as needed.

Explanation:

Step1: Recall the z - score formula

The formula for the z - score is \(z=\frac{x-\mu}{\sigma}\), where \(x\) is the data point, \(\mu\) is the mean, and \(\sigma\) is the standard deviation.

Step2: Substitute the given values into the formula

We are given that \(x = 13.7\), \(\mu=12.5\), and \(\sigma = 1.7\).
Substitute these values into the formula: \(z=\frac{13.7 - 12.5}{1.7}\).

Step3: Calculate the numerator

First, calculate \(13.7-12.5=1.2\). So the formula becomes \(z=\frac{1.2}{1.7}\).

Step4: Perform the division

\(z=\frac{1.2}{1.7}\approx0.71\) (rounded to the nearest hundredth).

Answer:

\(0.71\)