Question

Based on sample data, newborn males have weights with a mean of 3242.4 g and a standard deviation of 844.4 g. Newborn females have weights with a mean of 3095.9 g and a standard deviation of 508.6 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?

Answer 1

The formula for calculating z score is expressed as

z = (x - μ)/s

where

x is the sample mean

μ is the mean

s is the sample standard deviation

Considering the newborn males,

x = 1700

μ = 3242.4

s = 844.4

Thus,

z = (1700 - 3242.4)/844.4

z = - 1.83

Considering the newborn females,

x = 1700

μ = 3095.9

s = 508.6

Thus,

z = (1700 - 3095.9)/508.6

z = - 2.74

The most extreme value is the z score that is furthest from zero. It is z = - 2.74. Thus, the female who weighs 1700 g is more extreme relatively

Since the z score for the male is z = - 1.83 and the z score for the female is z = - 2.74, the female has the weight that is more extreme.