Problem
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 13.3 inches long. Round your answer to the nearest hundredth as needed. \[ z= \] How long is a fish that has a z-score of 1.2 ? Round your answer to the nearest tenth as needed. inches Question Help: Video Message instructor
Solution
Step 1 ：Calculate the z-score using the formula \( z = \frac{(X - \mu)}{\sigma} \)
Step 2 ：Substitute the given values into the formula: \( z = \frac{(13.3 - 12.5)}{1.7} \)
Step 3 ：Simplify the expression to find the z-score
Step 4 ：Round the z-score to the nearest hundredth
Step 5 ：\( \boxed{0.47} \)
