Question

Suppose babies born after a gestation period of 32 to 35 weeks have a mean weight of 3000 grams and a standard deviation of 900 grams while babies born after a gestation period of 40 weeks have a mean weight of 3500 grams and a standard deviation of 440 grams. If a 32​-week gestation period baby weighs 2575 grams and a 40​-week gestation period baby weighs 3075 ​grams, find the corresponding​ z-scores. Which baby weighs less relative to the gestation​ period? Find the corresponding​ z-scores. Which baby weighs relatively less​? Select the correct choice below and fill in the answer boxes to complete your choice. ​(Round to two decimal places as​ needed.)

A. The baby born in week 40 weighs relatively less since its​ z-score, __​, is larger than the​ z-score of __ for the baby born in week 32.

B. The baby born in week 32 weighs relatively less since its​ z-score, __​, is smaller than the​ z-score of __ for the baby born in week 40.

C. The baby born in week 40 weighs relatively less since its​ z-score, __​, is smaller than the​ z-score of __for the baby born in week 32.

D. The baby born in week 32 weighs relatively less since its​ z-score, __​, is larger than the​ z-score of __for the baby born in week 40.

Answer 1

Solution :

Given that ,

mean = = 3000

standard deviation =  = 900

x = 2575

Using z-score formula,

z = x - /   

z = 2575 - 3000 / 900

z = -0.47 (32 week)

mean = = 3500

standard deviation =  = 440

x = 3075

Using z-score formula,

z = x - /   

z = 3075 - 3500 / 440

z = -0.97 (40 week)

C. The baby born in week 40 weighs relatively less since its​ z-score, -0.97, is smaller than the​ z-score of -0.47 for the baby born in week 32.