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 :\( \boxed{0.47} \)

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Source: https://solvelyapp.com/problems/62nczgfnRq/

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