Respuesta :
Answer:
A birth weight of 3.9998kg has a z-score of 0.81.
Step-by-step explanation:
Problems of normally distributed samples can be 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.
In this problem, we have that:
[tex]\mu = 3.53, \sigma = 0.58[/tex]
What birth weight has a z-score of 0.81?
This is X when Z = 0.81. So:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]0.81 = \frac{X - 3.53}{0.58}[/tex]
[tex]X - 3.53 = 0.58*0.81[/tex]
[tex]Z = 3.9998[/tex]
A birth weight of 3.9998kg has a z-score of 0.81.
