My textbook had this question:
"Two swimmers, Angie and Beth, from different teams, wanted to find out who had the fastest time for the 50 meter freestyle when compared to her team. Which swimmer had the fastest time when compared to her team?"
\begin{array}{|c|c|c|c|} \hline Swimmer& Time (seconds) & Team Mean Time & Team Standard Deviation \\ \hline Angie& 26.2& 27.2& 0.8\\ \hline Beth& 27.3& 30.1& 1.4\\ \hline \end{array}
Now my textbook's answer was this:
"From the above scores, it is clear that Angie's time of -1.25 is smaller than Beth's time of -2. And for swimming, lower time is better. Therefore, Angie has a better swimming time as compared to her team."
What I did:
I calculate the number of standard deviations for both of them using the formula: z = $\frac{x - μ}{ σ}$. I then got Angie's z-score to be -1.25 and Beth's z-score to be -2. Now since Beth has a more negative z-score, doesn't that mean that she's deviating from her team's mean time, therefore having a faster time when compared to her team? I don't get why the textbook's answer is saying that Angela had the fastest time when compared to her team or did I do something wrong?
