Question

use z scores to compare the given values.
based on sample data, newborn males have weights with a mean of 3279.4 g and a standard deviation of 946.9 g. newborn females have weights with a mean of 3085.5 g and a standard deviation of 631.7 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=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: \(\mu = 3279.4\), \(\sigma=946.9\), \(x = 1500\)

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Step2: Calculate the z - score for the female

For the female: \(\mu = 3085.5\), \(\sigma = 631.7\), \(x = 1500\)

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Answer:

Since the z score for the male is \(z=-1.88\) and the z score for the female is \(z = - 2.51\), the female has the weight that is more extreme.