Question

Use z scores to compare the given values. Based on sample data, newborn males have weights with a mean of 3273.1 g and a standard deviation of 628.8 g. Newborn females have weights with a mean of 3026.1 g and a standard deviation of 624.8 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

After calculating the z-scores, it is determined that the 1700 g male newborn has a more extreme weight relative to his group with a z-score of -2.50, compared to the 1700 g female newborn with a z-score of -2.12.

Step-by-step explanation:

To determine which weight is more extreme relative to their respective groups, we calculate the z-scores for the male who weighs 1700 g and the female who weighs 1700 g, using their respective group's mean and standard deviation values.

For the male:
Z = (X - μ) / σ

Z = (1700 - 3273.1) / 628.8

Z ≈ -2.50

For the female:
Z = (X - μ) / σ

Z = (1700 - 3026.1) / 624.8

Z ≈ -2.12

A z-score represents the number of standard deviations an observation is from the mean. The male's z-score is approximately -2.50, and the female's is approximately -2.12. Since a z-score of -2.50 is farther from 0 than -2.12, the male's weight of 1700 g is more extreme relative to the group from which he came compared to the female with the same weight.