Answer :
Answer:
Tom did better relative to the performance of their classes.
Step-by-step explanation:
Problems of normally distributed samples can be solved using the z-score formula.
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]
This score how many standard deviations above or below the mean a measure is.
In this problem, whoever has the best Z score between Tom and Peter did better on the test relative to the performance of their classes.
Tom
Scored 77 out of a possible 100 on his midterm math examination. The distribution of the class had a mean of 68 and a standard deviation of 8.8.
So [tex]X = 77, \mu = 68, 8.8[/tex]
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{77 - 68}{8.8}[/tex]
[tex]Z = 1.02[/tex]
Peter
Scored 78 out of a possible 100. His class distribution had a mean of 68 and a standard deviation of 16.
So [tex]X = 78, \mu = 68, 16[/tex]
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{78 - 68}{16}[/tex]
[tex]Z = 0.625[/tex]
Tom had the higher Z score, so he did better relative to the performance of their classes.