Q:

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. Peter, who is in a different calculus class, scored 78 out of a possible 100. His class distribution had a mean of 68 and a standard deviation of 16. Relative to the performance of their classes, who did better?

Accepted Solution

A:
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.TomScored 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]PeterScored 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.