Respuesta :
Answer:
Due to the higher z-score, Jane did better in class.
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's grade had the better z-score did better in class.
Mary's:
Mean of 85, standard deviation of 5, grade of 88. This means that [tex]\mu = 85, \sigma = 5, X = 88[/tex]. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{88 - 85}{5}[/tex]
[tex]Z = 0.6[/tex]
Jane's
Mean of 80, standard deviation of 10, grade of 88. This means that [tex]\mu = 80, \sigma = 10, X = 88[/tex]. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{88 - 80}{10}[/tex]
[tex]Z = 0.8[/tex]
Due to the higher z-score, Jane did better in class.
