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. The standard is set so that all fish smaller than 70.20 centimeters or larger than 89.80 centimeters must be thrown back. What proportion of the population would be thrown back?

Question

Quizplus · Accepted Answer

We need to find the proportion of the population that falls outside the limits of 70.20 centimeters and 89.80 centimeters.

Using the z-score formula: 
z = (x - μ) / σ

For the lower limit: 
z = (70.20 - 80) / 5 = -1.96

For the upper limit: 
z = (89.80 - 80) / 5 = 1.96

Using a standard normal distribution table, the proportion of the population outside these limits is:

P(z < -1.96 or z > 1.96) = 0.05

Therefore, 5% of the population would be thrown back.

A Researcher Is Interested in the Lengths of Salvelinus Fontinalis