Question

use z scores to compare the given values.
based on sample data, newborn males have weights with a mean of 3254.4 g and a standard deviation of 571.1 g. newborn females have weights with a mean of 3004.2 g and a standard
deviation of 574.1 g. who has the weight that is more extreme relative to the group from which they came: a male who weighs 1700 g or a female who weighs 1700 g?
since the z score for the male is z = □ and the z score for the female is z = □, 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 \(z=\frac{x - \mu}{\sigma}\). For males, \(\mu = 3254.4\) g, \(\sigma=571.1\) g, and \(x = 1700\) g.

$$ z_{male}=\frac{1700 - 3254.4}{571.1}=\frac{- 1554.4}{571.1}\approx - 2.72 $$

Step2: Calculate the z - score for the female

For females, \(\mu = 3004.2\) g, \(\sigma = 574.1\) g, and \(x = 1700\) g.

$$ z_{female}=\frac{1700 - 3004.2}{574.1}=\frac{-1304.2}{574.1}\approx - 2.27 $$

Step3: Compare the absolute values of the z - scores

The absolute value of \(z_{male}\) is \(|z_{male}|=2.72\), and the absolute value of \(z_{female}\) is \(|z_{female}| = 2.27\). Since \(2.72>2.27\), the male has a more extreme weight.

Answer:

Since the z score for the male is \(z=-2.72\) and the z score for the female is \(z = - 2.27\), the male has the weight that is more extreme.