Question

Suppose babies born after a gestation period of 32 to 35 weeks have a mean weight of 25002500 grams and a standard deviation of 800800 grams while babies born after a gestation period of 40 weeks have a mean weight of 27002700 grams and a standard deviation of 375375 grams. If a 3232​-week gestation period baby weighs 20252025 grams and a 4040​-week gestation period baby weighs 22252225 ​grams, find the corresponding​ z-scores. Which baby weighs lessless relative to the gestation​ period?

Answer 1

Answer:

32-35 Week case

$z = \frac{2025-2500}{800}=-0.594$

40 week case

$z = \frac{2225-2700}{375}=-1.27$

For this case since the z score is lower (-1.27<-0.574) for the baby of 40 week this one would be the baby that weighs less relative to the gestation period

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

32-35 Week case

Let X the random variable that represent the weight, and for this case we know the distribution for X is given by:

$X \sim N(2500,800)$  

Where $\mu=2500$ and $\sigma=800$

The z score given by:

$z=\frac{x-\mu}{\sigma}$

And if w replace for the value of x=2025 we got:

$z = \frac{2025-2500}{800}=-0.594$

40 week case

Let X the random variable that represent the weight, and for this case we know the distribution for X is given by:

$X \sim N(2700,375)$  

Where $\mu=2700$ and $\sigma=375$

The z score given by:

$z=\frac{x-\mu}{\sigma}$

And if w replace for the value of x=2225 we got:

$z = \frac{2225-2700}{375}=-1.27$

For this case since the z score is lower (-1.27<-0.574) for the baby of 40 week this one would be the baby that weighs less relative to the gestation period