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=(1600-3286.7)/(925.1)=-1.82`

And now, for the female:

`Z=(1600-3090.4)/(538.7)=-2.766`

3) We can conclude then, that:

`Z_(male)=-1.82,Z_(female)=-2.766,the\: female`