Respuesta :
Answer:
The 35-week gestation period baby has a z-score of 0.7.
The 41-week gestation period baby has a z-score of 0.89
Since the 41-week gestation period baby has a higher z-score, he weighs more relatively to his gestation period.
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Which baby weighs more relative to the gestation period?
The baby with the higher z-score.
35-week gestation period baby weighs 2850 grams
Suppose babies born after a gestation period of 32 to 35 weeks have a mean weight of 2500 grams and a standard deviation of 500 grams
This means that Z is found when [tex]X = 2850, \mu = 2500, \sigma = 500[/tex]
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{2850 - 2500}{500}[/tex]
[tex]Z = 0.7[/tex]
The 35-week gestation period baby has a z-score of 0.7.
41-week gestation period baby weighs 3150 grams.
Babies born after a gestation period of 40 weeks have a mean weight of 2800 grams and a standard deviation of 395 grams.
This means that Z is found when [tex]X = 3150, X = 2800, \mu = 395[/tex]
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{3150 - 2800}{395}[/tex]
[tex]Z = 0.89[/tex]
The 41-week gestation period baby has a z-score of 0.89
Since the 41-week gestation period baby has a higher z-score, he weighs more relatively to his gestation period.
