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At a made-up school sports day, Mei jumps 6.2 m in the long jump, where the jumps have mean 5.8 m…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
At a made-up school sports day, Mei jumps 6.2 m in the long jump, where the jumps have mean 5.8 m and SD 0.25 m. Tomas runs 100 m in 12.1 s, where the times have mean 12.9 s and SD 0.4 s. Find each z-score. For running, a smaller time is better. Which athlete did better compared with the others in the same event?
Need a reminder? The key ideaShow
A z-score counts standard deviations from the mean and has no units. For mound-shaped data about , and lie within 1, 2 and 3 SDs.
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Step 1. Mei. .
Step 2. Tomas. .
Step 3. Compare. Mei jumped 1.6 SDs further than the mean. Tomas ran 2 SDs faster than the mean.
Answer: and . Tomas did better compared with his event.
Watch out. The units cancel in each z-score. That is what lets us compare metres with seconds at all.
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