Question

Use z scores to compare the given values.

Based on sample​ data, newborn males have weights with a mean of 3292.4 g and a standard deviation of 697.5 g. Newborn females have weights with a mean of 3000.6 g and a standard deviation of 727.9 g. Who has the weight that is more extreme relative to the group from which they​ came: a male who weighs 1500 g or a female who weighs 1500 ​g?
Since the z score for the male is z
equals
=


and the z score for the female is z
equals
=


​, the
female or male

has the weight that is more extreme.

Answer 1

Z for males = 2.57

Z for females = 2.06

male value is more extreme

Explanation:

Z score represents how many standard deviation you are from the mean.

The formula is:

Z = (Value - Mean)/(ST. DEV.)

For newborn males:

Z = (1500-3292.4)/697.5 = 2.57

For newborn females:

Z = (1500-3000.6)/727.9 = 2.06

Z score for newborn males is bigger, therefore 1500 is more extreme relative to the group