A researcher is interested in the lengths of Salvelinus fontinalis (brook trout), which are known to be approximately Normally distributed with mean 80 centimeters and standard deviation 5 centimeters. To help preserve brook trout populations, some regulatory standards need to be set limiting the size of fish that can be caught. To ensure that the smallest 8% of the brook trout get thrown back, what should the lower cut-off be?

Question

Quizplus · Accepted Answer

Using the Normal distribution table, we can find the z-score that corresponds to the smallest 8% of the distribution. This is equivalent to finding the z-score that encloses the lower 4% of the distribution (since the distribution is symmetric). Consulting the table, we find that the z-score is approximately -1.41. We can use the formula z = (x - mu) / sigma to solve for the lower cut-off x:
-1.41 = (x - 80) / 5
-7.05 = x - 80
x = 72.95
Therefore, to ensure that the smallest 8% of brook trout get thrown back, the lower cut-off should be approximately 72.95 centimeters.

A Researcher Is Interested in the Lengths of Salvelinus Fontinalis