Question

Suppose babies born after a gestation period of 32 to 35 weeks have a mean weight of 2800 grams and a standard deviation of 600 grams while babies bom after a gestation period of 40 weeks have a mean weight of 3400grams and a standard deviation of 425 grams. If a 34 -week gestation period baby weighs 2425 grams an 41-week gestation period baby woighs 3025 grams, find the corresponding z-scores. Which baby weighs less relative to the gestation period? Find the corresponding z.scores. Which baby weighe relatively less? Select the correct choice below and fill in the answer boxes to complete your choice. (Round to two derimal places as needed) A. The baby born in week 34 weighs relatively less since its z-score, is larger than the z-score of for the baby born in week 41. B. The baby born in week 41 weighs relatively less since its z−4core, is larger than the z-score of for the baby born in week 34 . C. The baby born in week 41 weighs relatively less since its z-acore, is simailer than the z-score of for the baby born in week 34 . D . The baby born in week 34 weighs relatively less since its z-score, is smaller than the z-score of for the baby born in week 41 .

Answer 1

To find the z-score, we can use the formula:

z = (x - μ) / σ

where x is the observed value, μ is the mean, and σ is the standard deviation.

For the 34-week gestation baby weighing 2425 grams:
z34 = (2425 - 2800) / 600
z34 ≈ -0.625

For the 41-week gestation baby weighing 3025 grams:
z41 = (3025 - 3400) / 425
z41 ≈ -0.882

Comparing the z-scores, we can see that the z34 score is smaller than the z41 score. This means that the baby born in week 34 weighs relatively less compared to the gestation period, as its z-score is smaller (closer to the mean) than the z-score for the baby born in week 41.

Therefore, the correct choice is:

D. The baby born in week 34 weighs relatively less since its z-score is smaller than the z-score for the baby born in week 41.