Question

In 2010, the average finishing time for marathons across the US was approximately 278 minutes, with a standard deviation of approximately 63 minutes. What finishing time defines the fastest 7.93% of runners?

Answer 1

336 minutes

Explanation:

Mean finishing time: 278 minutes

Standard Deviation: 63 minutes

Confidence interval: [278 - 63] , [278 + 63] = [215 , 341] minutes

What finishing time defines the fastest 7.93% of runners?

This means the 7.93% of time closest to the upper limit of 341 minutes

341 - 215 ≡ 63 × 2 = 126

7.93% of 126 = 0.0793 × 126 = 9.9918

341 - 9.9918 = 331.0082

Hence the finishing time that defines the fastest 7.93% of runners has an interval of [331 , 341] minutes with a mean or average of 336.0041 ≅ 336 minutes