Question

se z scores to compare the given values. Based on sample​ data, newborn males have weights with a mean of 3258.2 g and a standard deviation of 580.4 g. Newborn females have weights with a mean of 3093.6 g and a standard deviation of 643.6 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 and the z score for the female is zequals ​, the has the weight that is more extreme. ​(Round to two decimal​ places.)

Answer 1

Zscore for X = (X-Mean)/Standard deviation)

newborn males have weights with a mean of 3258.2 g and a standard deviation of 580.4 g

a male who weighs 1700 g

z score for the male who weighs 1700 g = (1700-Mean)/Standard deviation) = (1700-3258.2)/580.4 = - 1558.2 /580.4=-2.68

Newborn females have weights with a mean of 3093.6 g and a standard deviation of 643.6 g

a female who weighs 1700 ​g

z score for the female who weighs 1700 ​g = (1700-Mean)/Standard deviation) = (1700-3093.6)/643.6 = - 1393.6 /643.6=-2.17

z score for the male is -2.68

z score for the female is -2.17

Which ever z-score is farther away from '0' that's more extreme

-2.68 is farther away from '0' than -2.17

Hence a male who weighs 1700 g is more extreme

Or

Since , |Z-score of male | : |-2.68| : 2.68 > 2.17: |-2.17| : |Z-score or Female|

Hence a male who weighs 1700 g is more extreme