SOLUTION: The length of a certain kind of Colorado brook trout is normally distributed with a mean of 13.4 inches and a standard deviation of 1.4 inches.
What minimum size limit should th
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What minimum size limit should th
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Question 1191372: The length of a certain kind of Colorado brook trout is normally distributed with a mean of 13.4 inches and a standard deviation of 1.4 inches.
What minimum size limit should the Department of Natural Resources set if it wishes to allow people to keep 82 percent of the trout they catch? (Round your answer to 2 decimal places.)
Minimum size limit: ??? inches Answer by CPhill(1959) (Show Source):
You can put this solution on YOUR website! Here's how to determine the minimum size limit:
1. **Find the z-score:** We want to find the length below which 18% (100% - 82%) of the trout fall. We use a z-table or calculator to find the z-score corresponding to a cumulative probability of 0.82. A z-score of approximately 0.92 corresponds to 82% of the data.
2. **Use the z-score formula:**
x = μ + zσ
Where:
* x is the minimum size limit we want to find.
* μ is the mean length (13.4 inches).
* σ is the standard deviation (1.4 inches).
* z is the z-score (0.92).
3. **Calculate:**
x = 13.4 + (0.92 * 1.4)
x = 13.4 + 1.288
x ≈ 14.69 inches
Therefore, the Department of Natural Resources should set a minimum size limit of approximately 14.69 inches.
