Answer to Question #130546 in Statistics and Probability for Samuel kassapa

Question

A large college class is graded on a total points system. The total points earned in a semester by the students in the class vary normally with a mean of 675 and a standard deviation of 50. Another large class in a different department is graded on a 0 to 100 scale. The final grades in that class follow a normal model with a mean of 82 and a standard deviation of 6. Aseda earns 729 points in the first class, while Ayeyi scores 90 in the second class. Which student did better and why?

Answer 1

The criterion of better student performance in this case is deviation from the mean. The farther is student from the mean, the more outstanding he/she is. Let's calculate how far from the mean is each of students in terms of deviation.

For Aseda: $\frac{729-675}{50}=1.08$. So, $\sigma_1 = 1.08 \sigma_0$ .

For Ayeyi: $\frac{90-82}{6}=1.33$. So, $\sigma_2 = 1.33 \sigma_0$ .

Answer: Ayeyi did better, because her grade is $1.33 \sigma_0$ away from the mean. Aseda did worse, because her grade is only $1.08 \sigma_0$ away from the mean.