Respuesta :
Answer:
The 33 week gestation period baby has a zscore of -0.47.
The 41 week gestation period baby has a zscore of -0.94.
The 41 week gestation period baby weighs less 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 [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a value X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The zscore represents how many standard deviations the value of X is above or below the mean [tex]\mu[/tex]. This means that the baby with the lowest Zscore is the one who weighs relatively less to the gestation period.
33 week gestation period baby:
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, so [tex]\mu = 2700, \sigma = 900[/tex].
A 33​-week gestation period baby weighs 2275 grams. So [tex]X = 2275[/tex].
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{2275 - 2700}{900}[/tex]
[tex]Z = -0.47[/tex]
41 week gestation period baby:
Babies born after a gestation period of 40 weeks have a mean weight of 3200 grams and a standard deviation of 450 grams, so [tex]\mu = 3200, \sigma = 450[/tex]
A 41​-week gestation period baby weighs 2775 ​grams, so [tex]X = 2775[/tex].
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{2775 - 3200}{450}[/tex]
[tex]Z = -0.94[/tex]
The 41 week gestation period baby weighs less relative to the gestation period, since he has a lower zscore.
