Question

Jean's finishing time for the Boulder 10K race was 1.63 standard deviations faster than the woman's average for her age group. There were 385 women who ran in her age group. Assuming a normal distribution how many women ran faster than her?

Answer 1

In order to find the number of women that ran faster than her, we first need to look at the z-table for the corresponding value for a score of 1.63.

Looking at the table, we have a value of 0.9484, so we have that Jean is faster than 94.84% of the women.

That means she is in the top 5.16% faster women, and that corresponds to:

$0.0516\cdot385=19.866$

So Jean is in the top 20 faster women, that means we have 19 women faster than her.