Respuesta :
Answer:
The z-score for an ACT score of 26 is 0.17.
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 a particular year, the mean score on the ACT test was 25 and the standard deviation was 5.9.
This means that [tex]\mu = 25, \sigma = 5.9[/tex]
Find the z-score for an ACT score of 26.
This is Z when X = 26. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{26 - 25}{5.9}[/tex]
[tex]Z = 0.17[/tex]
The z-score for an ACT score of 26 is 0.17.
