Question

Use z scores to compare the given values.Based on sample data, newborn males have weights with a mean of 3286.7 g and a standard deviation of925.1 g. Newborn females have weights with a mean of 3090.4 g and a standard deviation of 538.7 g. Whohas the weight that is more extreme relative to the group from which they came: a male who weighs 1600 gor a female who weighs 1600 g?

Answer 1

$Z_{male}=-1.82,Z_{female}=-2.766,the\: \mathbf{female}\: has\: the\: weight\: that\: is\: more\: extreme$

1) Let's tackle this problem in parts.

The newborn males

μ= 3286.7

σ=925.1

The newborn females

μ= 3090.4

σ=538.7

2) So, let's find the Z scores for the male representative, a male with 1600g and :

$Z=\frac{1600-3286.7}{925.1}=-1.82$

And now, for the female:

$Z=\frac{1600-3090.4}{538.7}=-2.766$

3) We can conclude then, that:

$Z_{male}=-1.82,Z_{female}=-2.766,the\: female$