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 be offered the job.
Alissa:
[tex]X = 68.5, \mu = 60.4, \sigma = 9[/tex]
So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{68.5 - 60.4}{9}[/tex]
[tex]Z = 0.9[/tex]
Morgan:
[tex]X = 252.5, \mu = 227, \sigma = 17[/tex]
So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{252.5 - 227}{17}[/tex]
[tex]Z = 1.5[/tex]
Norma:
[tex]X = 7.96, \mu = 6.7, \sigma = 0.7[tex]
So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{7.96 - 6.7}{0.7}[/tex]
[tex]Z = 1.8[/tex]
Due to the higher Z-score, Norma should be offered the job
