Question

use z scores to compare the given values.
based on sample data, newborn males have weights with a mean of 3297.9 g and a standard deviation of 787.8 g. newborn females have weights with a mean of 3052.1 g and a standard deviation of 565.9 g. who has the weight that is more extreme relative to the group from which they came: a male who weighs 1600 g or a female who weighs 1600 g?
since the z score for the male is ( z = square ) and the z score for the female is ( z = square ), the has the weight that is more extreme.
(round to two decimal places.)

Explanation:

Step1: Calculate the z - score for the male

The formula for the z - score is \(z=\frac{x-\mu}{\sigma}\), where \(x\) is the value, \(\mu\) is the mean, and \(\sigma\) is the standard deviation.
For the male: \(\mu = 3297.9\), \(\sigma=787.8\), \(x = 1600\)
\(z_{male}=\frac{1600 - 3297.9}{787.8}=\frac{- 1697.9}{787.8}\approx - 2.15\)

Step2: Calculate the z - score for the female

For the female: \(\mu = 3052.1\), \(\sigma = 565.9\), \(x = 1600\)
\(z_{female}=\frac{1600-3052.1}{565.9}=\frac{-1452.1}{565.9}\approx - 2.56\)

Answer:

Since the z - score for the male is \(z=-2.15\) and the z - score for the female is \(z = - 2.56\), the female has the weight that is more extreme.