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?

32-35 Week case

40 week case

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:

Where and

The z score given by:

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

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:

Where and

The z score given by:

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

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

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step-by-step explanation:

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