To qualify as a contestant in a race, a runner has to be in the top 16% of all entrants. The running times are normally distributed, with a mean of 63 min and a standard deviation of 4 min. To the nearest minute, what is the qualifying time for the race

Question

Karla Hunt

Mathematics

14 October, 03:02

To qualify as a contestant in a race, a runner has to be in the top 16% of all entrants. The running times are normally distributed, with a mean of 63 min and a standard deviation of 4 min. To the nearest minute, what is the qualifying time for the race

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Julien Friedman · Answer 1

Find P (z) = 16% where z = (t-63) / 4

And from the Normal Distribution tables you find that a left tail of 16% implies z=-0,9945 then:

t=-4 x 0.9945 + 63=59.22 and the solution would be 59 minutes