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In a made-up fitness test, each runner's time for 1 km is recorded as the number of seconds over 4…

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In a made-up fitness test, each runner's time for 1 km is recorded as the number of seconds over 4 minutes. These recorded values have a mean of 70 s and a standard deviation of 6 s. Find the z-score of a runner who records 85 and of a runner who records 61. Which runner was faster than average?

Need a reminder? The key ideaShow

A z-score counts standard deviations from the mean and has no units. For mound-shaped data about $68\%$ , $95\%$ and $99.7\%$ lie within 1, 2 and 3 SDs.

\displaystyle z = \dfrac{x - \text{mean}}{\text{SD}}

The worked solution

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