Question

Suppose babies born after a gestation period of 32 to 35 weeks have a mean weight of 2700 grams and a standard deviation of 900 grams while babies born after a gestation period of 40 weeks have a mean weight of 3200 grams and a standard deviation of 450 grams. If a 33​-week gestation period baby weighs 2275 grams and a 41​-week gestation period baby weighs 2775 ​grams, find the corresponding​ z-scores. Which baby weighs less relative to the gestation​ period?

Answer 1

Answer:

The 33 week gestation period baby has a zscore of -0.47.

The 41 week gestation period baby has a zscore of -0.94.

The 41 week gestation period baby weighs less relative to the gestation period.

Step-by-step explanation:

Normal model problems can be solved by the zscore formula.

On a normaly distributed set with mean $\mu$ and standard deviation $\sigma$, the z-score of a value X is given by:

$Z = \frac{X - \mu}{\sigma}$

The zscore represents how many standard deviations the value of X is above or below the mean $\mu$. This means that the baby with the lowest Zscore is the one who weighs relatively less to the gestation period.

33 week gestation period baby:

Babies born after a gestation period of 32 to 35 weeks have a mean weight of 2700 grams and a standard deviation of 900 grams, so $\mu = 2700, \sigma = 900$.

A 33​-week gestation period baby weighs 2275 grams. So $X = 2275$.

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{2275 - 2700}{900}$

$Z = -0.47$

41 week gestation period baby:

Babies born after a gestation period of 40 weeks have a mean weight of 3200 grams and a standard deviation of 450 grams, so $\mu = 3200, \sigma = 450$

A 41​-week gestation period baby weighs 2775 ​grams, so $X = 2775$.

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{2775 - 3200}{450}$

$Z = -0.94$

The 41 week gestation period baby weighs less relative to the gestation period, since he has a lower zscore.