Question

suppose babies born after a gestation period of 32 to 35 weeks have a mean weight of 2500 grams and a standard deviation of 600 grams while babies born after a gestation period of 40 weeks have a mean weight of 2800 grams and a standard deviation of 410 grams. if a 32 - week gestation period baby weighs 2750 grams and a 40 - week gestation period baby weighs 3050 grams, find the corresponding z - scores. which baby weighs more relative to the gestation period? answer boxes to complete your choice. (round to two decimal places as needed.) a. the baby born in week 32 weighs relatively more since its z - score, , is larger than the z - score of , for the baby born in week 40. b. the baby born in week 40 weighs relatively more since its z - score, , is larger than the z - score of , for the baby born in week 32. c. the baby born in week 32 weighs relatively more since its z - score, , is smaller than the z - score of , for the baby born in week 40. d. the baby born in week 40 weighs relatively more since its z - score, , is smaller than the z - score of , for the baby born in week 40.

Explanation:

Step1: Recall the z - score formula

The z - score formula is $z=\frac{x-\mu}{\sigma}$, where $x$ is the value, $\mu$ is the mean, and $\sigma$ is the standard deviation.

Step2: Calculate z - score for 32 - week baby

For 32 - week babies, $\mu = 2500$ grams and $\sigma=600$ grams, and $x = 3050$ grams. Then $z_1=\frac{3050 - 2500}{600}=\frac{550}{600}\approx0.92$.

Step3: Calculate z - score for 40 - week baby

For 40 - week babies, $\mu = 2800$ grams and $\sigma = 410$ grams, and $x = 2750$ grams. Then $z_2=\frac{2750 - 2800}{410}=\frac{- 50}{410}\approx - 0.12$.

Step4: Compare z - scores

Since $z_1=0.92$ and $z_2=-0.12$, and $0.92>-0.12$, the 32 - week baby weighs more relative to its group because its z - score is larger.

Answer:

A. The baby born in week 32 weighs relatively more since its z - score, 0.92, is larger than the z - score of - 0.12 for the baby born in week 40.