Suppose babies born after a gestation period of 32 to 35 weeks have a mean weight of 2500 grams and a standard deviation of 700 grams while babies born after a gestation period of 40 weeks have a mean weight of 3000 grams and a standard deviation of 475 grams. if a 34-week gestation period baby weighs 2975 grams and a 41-week gestation period baby weighs 3475 grams, find the corresponding z-scores. which baby weighs more relative to the gestation period?

The 41 week gestation's period baby has a higher zscore, so he weighs more 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 and standard deviation , the z-score of a value X is given by:

The zscore represents how many standard deviations the value of X is above or below the mean .

In this problem, whichever baby has the higher zscore is the one who weighs more relative to the gestation period.

Babies born after a gestation period of 32 to 35 weeks have a mean weight of 2500 grams and a standard deviation of 700 grams. A 34-week gestation period baby weighs 2975.

Here, we have .

So

Babies born after a gestation period of 32 to 35 weeks have a mean weight of 3000 grams and a standard deviation of 475 grams. A 41-week gestation period baby weighs 3475.

Here, we have .

So

The 41 week gestation's period baby has a higher zscore, so he weighs more relative to the gestation period.