Question

There was a junior and senior division for the runners in the Friendly 5K Race. Two friends, Boomer and Paulina,
argued about who was faster, relative to their divisions. In the junior division, Boomer had a standardized score of z =-
0.23, while in the senior division, Paulina's standardized score was z = -0.28. Which of the following best describes the
conclusion between the two friends?
Because Boomer has a larger standardized score, he did better relative to his division than Paulina.
Because Boomer has a smaller standardized score, he did better relative to his division than Paulina.
Because Boomer has a larger standardized score, Paulina did better relative to her division than Boomer.
Because Boomer has a smaller standardized score, Paulina did better relative to her division than Boomer.
Because the standardized scores are essentially the same, Boomer and Paulina tied each other, relative to their
divisions.

Answer 1

Answer:

The correct option is;

Because Boomer has a larger standardized score, he did better relative to his division than Paulina

Step-by-step explanation:

The standard score of Boomer in the junior division = -0.23

The standard score of Paulina in the senior division = -0.28

We note that the standard score is the same as the z-score which is given as follows;

$Z=\dfrac{x-\mu }{\sigma }$

Where;

μ = The mean or average score (average speed of the runners in a division)

x = The recorded score (the speed recorded by a given runner)

σ = The standard deviation of the data set (of the division)

Therefore, given that we have;

The standard score of Boomer in the junior division = -0.23

The standard score of Paulina in the senior division = -0.28

Therefore, since -0.23 > -0.28, we have;

The standard score of Boomer > The standard score of Paulina

Which gives;

Because Boomer has a larger standardized score, he did better relative to his division than Paulina

Answer 2

Answer:

Because Boomer has a larger standardized score, he did better relative to his division than Paulina.

Explanation:

On the z-table, Boomers score is 59.10% and Paulina’s score is 38.97%. Boomer’s score is larger.