Respuesta :
Answer:
The z-score of the 32 week gestation period baby is -0.25.
The z-score of the 40 week gestation period baby is -0.42.
The 40 week gestation period baby has the lower z-score, so he weighs less relative to the 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 less relative to the gestation period?
Whoever has the lower z-score.
32 week baby:
Mean weight of 2900 grams and a standard deviation of 800 grams. 32-week gestation period baby weighs 2700 grams. We have to find Z when [tex]X = 2700, \mu = 2900, \sigma = 800[/tex]. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{2700 - 2900}{800}[/tex]
[tex]Z = -0.25[/tex]
The z-score of the 32 week gestation period baby is -0.25.
40 week baby:
Mean weight of 3200 grams and a standard deviation of 475 grams. 40-week gestation period baby weighs 3000 grams. We have to find Z when [tex]X = 3000, \mu = 3200, \sigma = 475[/tex]. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{3000 - 3200}{475}[/tex]
[tex]Z = -0.42[/tex]
The z-score of the 40 week gestation period baby is -0.42.
The 40 week gestation period baby has the lower z-score, so he weighs less relative to the gestation period.
