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

Mathematics

Jakayla Pitts

6 November, 02:15

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

+2

Answers (1)

Know the Answer?

Rylie Bradford · 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