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 3000 grams and a standard deviation of 430 grams. If a 32​-week gestation period baby weighs 2900 grams and a 41​-week gestation period baby weighs 3200 ​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 41 weighs relatively more since its​ z-score, enter your response here​, is larger than the​ z-score of enter your response here for the baby born in week 32.
B. The baby born in week 41 weighs relatively more since its​ z-score, enter your response here​, is smaller than the​ z-score of enter your response here for the baby born in week 32.
C. The baby born in week 32 weighs relatively more since its​ z-score, enter your response here​, is larger than the​ z-score of enter your response here for the baby born in week 41.
D. The baby born in week 32 weighs relatively more since its​ z-score, enter your response here​, is smaller than the​ z-score of enter your response here for the baby born in week 41.

Answer 1

The 32 week gestation's period baby weighs 0.31 standard deviations below the mean.

The 41 week gestation's period baby weighs 0.65 standard deviations below the mean.

The 41 week gestation's period baby weighs relatively less.

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 .

Find the corresponding z-scores.

Babies born after a gestation period of 32 to 35 weeks have a mean weight of 2700 grams and a standard deviation of 800 grams. A 32-week gestation period baby weighs 2450.

Here, we have .

So

A negative z-score indicates that the value is below the mean.

So, the 32 week gestation's period baby weighs 0.31 standard deviations below the mean.

Babies born after a gestations period of 40 weeks have a mean weight of 2900 grams and a standard deviation of 385 grams. A 41 week gestation period baby weights 2650 grams.

Here, we have

So, the 41 week gestation's period baby weighs 0.65 standard deviations below the mean.

Which baby weighs relatively less?

The 41 week gestation's period baby has a lesser z-score, so this means that he weighs relatively less.