Question

An elementary school class ran 1 mile in an average of 11 minutes with a standard deviation of 3 minutes. Rachel, a student in the class, ran 1 mile in 8 minutes. A junior high school class ran 1 mile in an average of 9 minutes, with a standard deviation of 2 minutes. Kenji, a student in the class, ran 1 mile in 8.5 minutes. A high school class ran 1 mile in an average of 7 minutes with a standard deviation of 4 minutes. Nedda, a student in the class, ran 1 mile in 8 minutes. Who is the fastest runner with respect to his or her class?

Answer 1

Answer:

Rachel

Step-by-step explanation:

We need to measure how far (towards the left) are the students from the mean in “standard deviations units”.  

That is to say, if t is the time the student ran the mile and s is the standard deviation of the class, we must find an x such that

mean - x*s = t

For Rachel we have

11 - x*3 = 8, so x = 1.  

Rachel is 1 standard deviation far (to the left) from the mean of her class

For Kenji we have

9 - x*2 = 8.5, so x = 0.25

Kenji is 0.25 standard deviations far (to the left) from the mean of his class

For Nedda we have

7 - x*4 = 8, so x = 0.25

Nedda is also 0.25 standard deviations far (to the left) from the mean of his class.

As Rachel is the farthest from the mean of her class in term of standard deviations, Rachel is the fastest runner with respect to her class.