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. What lower limit should the State Game Commission set on length if it is desired that 80 percent of the catch may be kept by fishers?
A)12.80 inches
B)11.48 inches
C)12.00 inches
D)9.22 inches Using Excel =NORM.INV(.20,14,3) = 11.475, or X = 14 - 0.84(3) = 11.48 using AppendixC.

Question

Quizplus · Accepted Answer

To find the lower limit, we need to find the value of x such that 80% of the distribution is above x. Using the normal distribution table or Excel function, we can find the z-score corresponding to the 20th percentile (since we want the 80th percentile to be above our lower limit).

Excel function: =NORM.INV(0.20, 14, 3) = -0.84

Next, we can use the z-score formula to find the corresponding value of x:

x = µ + zσ 
x = 14 + (-0.84)(3)
x = 11.48

Therefore, the State Game Commission should set a lower limit of 11.48 inches. Choice B is the correct answer.

The Lengths of Brook Trout Caught in a Certain Colorado