Question

1. suppose babies born after a gestation period of 32 to 35 weeks have a mean weight of 2500 grams and a standard deviation of 800 grams while babies born after a gestation period of 40 weeks have a mean weight of 2800 grams and a standard deviation of 395 grams. if a 32 - week - gestation - period baby weighs 2125 grams and a 41 - week - gestation - period baby weighs 2425 grams, find the corresponding z - scores. which baby weighs less relative to the gestation period?

Explanation:

Step1: Recall z - score formula

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

Step2: Calculate z - score for 32 - week baby

For a 32 - week baby with $x = 2125$ grams, $\mu=2800$ grams and $\sigma = 800$ grams.
$z=\frac{2125 - 2800}{800}=\frac{- 675}{800}=-0.84375$

Step3: Calculate z - score for 40 - week baby

For a 40 - week baby with $x = 2425$ grams, $\mu = 2500$ grams and $\sigma=395$ grams.
$z=\frac{2425 - 2500}{395}=\frac{-75}{395}\approx - 0.19$

Answer:

The z - score for the 32 - week baby is approximately $-0.84$ and the z - score for the 40 - week baby is approximately $-0.19$