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

Question

Quizplus · Accepted Answer

To find the lower limit for the top 80% of the distribution, we need to find the 20th percentile of a normal distribution with a mean of 14 inches and a standard deviation of 3 inches. Using the z-table, the z-score for the 20th percentile is approximately -0.84. Applying the formula: X = μ + zσ, we get X = 14 + (-0.84)(3) = 11.48 inches.

The Lengths of Brook Trout Caught in a Certain Colorado