Question

use z scores to compare the given values. based on sample data, newborn males have weights with a mean of 3233.9 g and a standard deviation of 633.5 g. newborn females have weights with a mean of 3027.7 g and a standard deviation of 687.3 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 = and the z score for the female is z =, the has the weight that is more extreme. (round to two decimal places.)

Explanation:

Step1: Recall z - score formula

The z - score formula is $z=\frac{x-\mu}{\sigma}$, where $x$ is the data value, $\mu$ is the mean, and $\sigma$ is the standard deviation.

Step2: Calculate z - score for male

For a male, $\mu = 3233.9$ g, $\sigma=633.5$ g, and $x = 1600$ g.
$z_{male}=\frac{1600 - 3233.9}{633.5}=\frac{- 1633.9}{633.5}\approx - 2.58$

Step3: Calculate z - score for female

For a female, $\mu = 3027.7$ g, $\sigma = 687.3$ g, and $x = 1600$ g.
$z_{female}=\frac{1600 - 3027.7}{687.3}=\frac{-1427.7}{687.3}\approx - 2.08$

Step4: Compare z - scores

The magnitude of $z_{male}\approx2.58$ and the magnitude of $z_{female}\approx2.08$. Since $2.58>2.08$, the male has a more extreme weight.

Answer:

Since the z - score for the male is $z=-2.58$ and the z - score for the female is $z = - 2.08$, the male has the weight that is more extreme.