The lengths of brook trout caught in a certain Colorado stream are normally distributed with a mean of 14 inches and a standard deviation of 3 inches. The first quartile for the lengths of brook trout would be: A)16.01 inches. B)11.00 inches. C)11.98 inches. D)10.65 inches.Using Excel =NORM.INV(.25,14,3) = 11.98, or Q₁ = 14 - 0.675(3) = 11.975 using AppendixC.

Question

Quizplus · Accepted Answer

Since the lengths of brook trout are normally distributed, we can use the z-score formula to find the first quartile. The z-score corresponding to the first quartile is -0.675. Using the formula:

z = (x - μ) / σ

where x is the first quartile, μ is the mean, and σ is the standard deviation, we can solve for x:

-0.675 = (x - 14) / 3

x - 14 = -2.025

x = 11.975

Therefore, the first quartile for the lengths of brook trout is approximately 11.98 inches.

The Lengths of Brook Trout Caught in a Certain Colorado