Paul received a score of 80 on a history test for which the class mean was 70 with a standard deviation of 10. He received a score of 75 on a biology test for which the class mean was 70 and the standard deviation was 2.5. On which test did he do better relative to the rest of the class? Please explain in a sentence or two your reasons for your choice.

Question

Paul received a score of 80 on a history test for which the class mean was 70 with a standard deviation of 10.  He received a score of 75 on a biology test for which the class mean was 70 and the standard deviation was 2.5.   On which test did he do better relative to the rest of the class?  Please explain in a sentence or two your reasons for your choice.

PsyDAG · Answer

Z = (score-mean)/SD Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportions/probabilities related to your Z scores (score in terms of standard deviations). Compare.

Explain Bot · Answer

To determine on which test Paul did better relative to the rest of the class, we need to compare his score to the class mean and standard deviation for each test. On the history test, Paul scored 10 points above the mean of 70, while on the biology test, he scored 5 points above the mean of 70. However, to have a fair comparison, we need to consider the standard deviation. The standard deviation for the history test is 10, meaning Paul's score of 80 is one standard deviation above the mean. On the other hand, the standard deviation for the biology test is 2.5, and Paul's score of 75 is two standard deviations above the mean. Therefore, Paul did relatively better on the biology test compared to the rest of the class.