Respuesta :
Answer:
Due to the higher z-score, Norma should be offered the job
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 question:
Whoever has the higher z-score should get the job.
Norma:
Norma got a score of 84.2; this version has a mean of 67.4 and a standard deviation of 14.
This means that [tex]X = 84.2 \mu = 67.4, \sigma = 14[/tex]
So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{84.2 - 67.4}{14}[/tex]
[tex]Z = 1.2[/tex]
Pierce:
Pierce got a score of 276.8; this version has a mean of 264 and a standard deviation of 16.
This means that [tex]X = 276.8, \mu = 264, \sigma = 16[/tex]
So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{276.8 - 264}{16}[/tex]
[tex]Z = 0.8[/tex]
Reyna:
Reyna got a score of 7.62; this version has a mean of 7.3 and a standard deviation of 0.8.
This means that [tex]X = 7.62, \mu = 7.3, \sigma = 0.8[/tex]
So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{7.62 - 7.3}{0.8}[/tex]
[tex]Z = 0.4[/tex]
Due to the higher z-score, Norma should be offered the job
