Respuesta :
Answer:
Test scores of 10.2 or lower are significantly low.
Test scores of 31 or higher are significantly high
Step-by-step explanation:
Z-score:
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 = 20.6, \sigma = 5.2[/tex]
Significantly low:
Z-scores of -2 or lower
So scores of X when Z = -2 or lower
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-2 = \frac{X - 20.6}{5.2}[/tex]
[tex]X - 20.6 = -2*5.2[/tex]
[tex]X = 10.2[/tex]
Test scores of 10.2 or lower are significantly low.
Significantly high:
Z-scores of 2 or higher
So scores of X when Z = 2 or higher
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]2 = \frac{X - 20.6}{5.2}[/tex]
[tex]X - 20.6 = 2*5.2[/tex]
[tex]X = 31[/tex]
Test scores of 31 or higher are significantly high
