Respuesta :
Answer:
The z-score for a person whose self-esteem score was 101.6 would be of -0.227.
Step-by-step explanation:
Z-score:
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score 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 p-value, we get the probability that the value of the measure is greater than X.
Gibson (1986) asked a sample of college students to complete a self-esteem scale on which the midpoint of the scale was the score 108.
This means that [tex]\mu = 108[/tex]
The standard deviation of self-esteem scores was 28.15
This means that [tex]\sigma = 28.15[/tex]
What would the z score be for a person whose self-esteem score was 101.6
This is Z when X = 101.6. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{101.6 - 108}{28.15}[/tex]
[tex]Z = -0.227[/tex]
The z-score for a person whose self-esteem score was 101.6 would be of -0.227.
