Question

suppose babies born after a gestation period of 32 to 35 weeks have a mean weight of 2900 grams and a standard deviation of 900 grams while babies born after a gestation period of 40 weeks have a mean weight of 3400 grams and a standard deviation of 535 grams. if a 32 - week gestation period baby weighs 3350 grams and a 40 - week gestation period baby weighs 3850 grams, find the corresponding z - scores. which baby weighs more relative to the gestation period?
find the corresponding z - scores. which baby weighs relatively more? 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 more since its z - score, , is larger than the z - score of for the baby born in week 32.
b. 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 32.
c. 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.
d. 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.

Explanation:

Step1: Calculate z - score for 32 - week baby

The formula for z - score is \(z=\frac{x-\mu}{\sigma}\), where \(x\) is the data point, \(\mu\) is the mean, and \(\sigma\) is the standard deviation.
For 32 - week baby: \(x = 3350\), \(\mu=2900\), \(\sigma = 900\)
\(z_1=\frac{3350 - 2900}{900}=\frac{450}{900}=0.50\)

Step2: Calculate z - score for 40 - week baby

For 40 - week baby: \(x = 3850\), \(\mu = 3400\), \(\sigma=535\)
\(z_2=\frac{3850 - 3400}{535}=\frac{450}{535}\approx0.84\)

Answer:

C. The baby born in week 32 weighs relatively more since its z - score, \(0.50\), is larger than the z - score of \(0.84\) for the baby born in week 40.