Respuesta :
Answer:
a) The Z-score for Patricia's test grade is 0.32.
b) The z-score for Whitney's test grade is of 0.34.
c) Due to the higher z-score, Whitney's did relatively better.
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.
a. Calculate the Z-score for Patricia's test grade.
Patricia took a test in English and earned a 76.5. Students' test grades in the English class had a mean of 73.1 and a standard deviation of 10.5.
This means that [tex]X = 76.5, \mu = 73.1, \sigma = 10.5[/tex]
The z-score is:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{76.5 - 73.1}{10.5}[/tex]
[tex]Z = 0.32[/tex]
The Z-score for Patricia's test grade is 0.32.
b. Calculate the z-score for Whitney's test grade.
Whitney took a test in Math and earned a 64.5. Students' test grades in Math had a mean of 60.9 and a standard deviation of 10.7.
This means that [tex]X = 64.5, \mu = 60.9, \sigma = 10.7[/tex]
The z-score is:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{64.5 - 60.9}{10.7}[/tex]
[tex]Z = 0.34[/tex]
The z-score for Whitney's test grade is of 0.34.
c. Which person did relatively better?
Due to the higher z-score, Whitney's did relatively better.
