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 700 grams while babies born after a gestation period of 40 weeks have a mean weight of 3400 grams and a standard deviation of 445 grams. if a 32 - week gestation period baby weighs 2950 grams and a 41 - week gestation period baby weighs 3550 grams, find the corresponding z - scores. which baby weighs more relative to the gestation period? 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 32 weighs relatively more since its z - score, , is smaller than the z - score of for the baby born in week 41. b. the baby born in week 41 weighs relatively more since its z - score, , is smaller than the z - score of for the baby born in week 32. c. the baby born in week 41 weighs relatively more since its z - score, , is larger than the z - score of for the baby born in week 32. d. 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 41.

Explanation:

Step1: Recall z - score formula

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

Step2: Calculate z - score for 32 - week baby

For 32 - week babies, $\mu = 2800$ grams and $\sigma=700$ grams, and $x = 2950$ grams. Then $z_1=\frac{2950 - 2800}{700}=\frac{150}{700}\approx0.21$.

Step3: Calculate z - score for 41 - week baby

For 41 - week babies, $\mu = 3400$ grams and $\sigma = 445$ grams, and $x = 3550$ grams. Then $z_2=\frac{3550 - 3400}{445}=\frac{150}{445}\approx0.34$.

Step4: Compare z - scores

Since $0.34>0.21$, the 41 - week baby weighs relatively more because its z - score is larger.

Answer:

B. The baby born in week 41 weighs relatively more since its z - score, 0.34, is larger than the z - score of 0.21 for the baby born in week 32.