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.

Question

Quizplus · Accepted Answer

The first quartile is the 25th percentile, which can be found using z-score formula:

z = (x - mean) / standard deviation

For the first quartile, we want to find the value of x such that 25% of the data is below it. Using a standard normal distribution table, we can find the z-score that corresponds to the 25th percentile:

z = -0.674

Substituting the values for mean and standard deviation:

-0.674 = (x - 14) / 3

Solving for x:

x = -0.674 * 3 + 14 = 11.98

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

The Lengths of Brook Trout Caught in a Certain Colorado