Answer :
Answer:
Z scores of -2 or lower are considered unusually low. Since the z-score of a 49-cm head circunference is -2, it is an unusual measure.
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.
Z scores of -2 or lower are considered unusually low, and zscores of 2 or higher are considered unusually high.
In this problem, we have that:
[tex]\mu = 55, \sigma = 3[/tex]
49cm head circunference unusual?
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{49 - 55}{3}[/tex]
[tex]Z = -2[/tex]
Z scores of -2 or lower are considered unusually low. Since the z-score of a 49-cm head circunference is -2, it is an unusual measure.