The weights of 6-week-old poults (juvenile turkeys) are normally distributed with a mean 8.5 pounds and standard deviation 1.4 pounds. Find the first quartile of the weight.
A) 6.05 lb
B) 9.07 lb
C) 6.80 lb
D) 7.56 lb

Question

Quizplus · Accepted Answer

The first quartile (Q1) corresponds to the 25th percentile of a distribution. In a normal distribution, this can be found using the Z-score formula for the percentile in question. The Z-score for the 25th percentile is approximately -0.675. Using the formula $Q1 = \mu + Z(\sigma)$, where $\mu$ is the mean (8.5 pounds) and $\sigma$ is the standard deviation (1.4 pounds), we calculate $Q1 = 8.5 + (-0.675)(1.4) = 8.5 - 0.945 = 7.555$, which rounds to 7.56 pounds.

The Weights of 6-Week-Old Poults (Juvenile Turkeys) Are Normally Distributed