Question

Use z scores to compare the given values. Based on sample​ data, newborn males have weights with a mean of 3259.6 g and a standard deviation of 722.4 g. Newborn females have weights with a mean of 3031.2 g and a standard deviation of 495.9 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 zequals nothing and the z score for the female is zequals nothing​, the female female male has the weight that is more extreme.

Answer 1

Since the z score for the male is z=-2.1589 and the z score for the female is z=-2.6844​, the female has the weight that is more extreme.

Explanation:

To find the z score, we use the following equation:

`z=(x-m)/(s)`

Where m is the mean and s is the standard deviation.

So, the z score for a male who weighs 1700 g is:

`z=(1700-3259.6)/(722.4)=-2.1589`

At the same way, the z score for a female who weighs 1700 g is:

`z=(1700-3031.2)/(495.9)=-2.6844`

Finally, -2.6844 is farther from zero than -2.1589, so the female has the weight that is more extreme.