Question

use z scores to compare the given values.
based on sample data, newborn males have weights with a mean of 3278.2 g and a standard deviation of 898.4 g. newborn females have weights with a mean of 3005.9 g a standard deviation of 565.3 g. who has the weight that is more extreme relative to the group from which they came: a male who weighs 1500 g or a female who weighs 1500 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 \(z=\frac{x-\mu}{\sigma}\), where \(x\) is the value, \(\mu\) is the mean, and \(\sigma\) is the standard deviation.
For the male: \(\mu = 3278.2\), \(\sigma=898.4\), \(x = 1500\)
\(z_{male}=\frac{1500 - 3278.2}{898.4}=\frac{- 1778.2}{898.4}\approx - 1.98\)

Step2: Calculate the z - score for the female

For the female: \(\mu = 3005.9\), \(\sigma = 565.3\), \(x = 1500\)
\(z_{female}=\frac{1500-3005.9}{565.3}=\frac{-1505.9}{565.3}\approx - 2.66\)

Answer:

Since the z - score for the male is \(z=-1.98\) and the z - score for the female is \(z = - 2.66\), the female has the weight that is more extreme.