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. What is the probability of catching a brook trout less than 72 centimeters in length?

Question

Quizplus · Accepted Answer

We need to find the probability of catching a brook trout less than 72 centimeters in length. We can standardize this using the z-score formula: z=(x-μ)/σ, where x is the value we are interested in, μ is the mean, and σ is the standard deviation. Thus, z=(72-80)/5=-1.6. We can now use a standard Normal table or calculator to find the probability of a z-score less than -1.6, which is 0.0548 (or approximately 0.055). Therefore, the answer is A.

A Researcher Is Interested in the Lengths of Salvelinus Fontinalis