Respuesta :
Answer:
The Z-score for an ACT score of 26 is 1.26.
Step-by-step explanation:
Problems of normally distributed samples(bell-shaped) 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.
(a) Find the z-score for an ACT score of 26.
In a particular year, the mean score on the ACT test was 19.3 and the standard deviation was 5.3. This means that [tex]\mu = 19.3, \sigma = 5.3[/tex]
So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{26 - 19.3}{5.3}[/tex]
[tex]Z = 1.26[/tex]
The Z-score for an ACT score of 26 is 1.26.
