To qualify as a contestant in a race, a runner has to be in the fastest 16% of all applicants. 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

To qualify as a contestant in a race, a runner has to be in the fastest 16% of all applicants.  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?

anonymous · Answer

@jim_thompson5910 can you help?

jim_thompson5910 · Answer

" the fastest 16% " means the top 16%

put another way, this person has to be faster than 100-16 = 84% of the other runners

jim_thompson5910 · Answer

you have to find the z-score that has an area of 0.84 (area under the curve to the left of this score)

anonymous · Answer

How do you find the z-score?

jim_thompson5910 · Answer

actually there's another way do this

jim_thompson5910 · Answer

have you learned about the empirical rule?

anonymous · Answer

no

jim_thompson5910 · Answer

the idea that 

68% of the distribution is within 1 std dev
95% of the distribution is within 2 std dev
99.7% of the distribution is within 3 std dev

sound familiar?

anonymous · Answer

oh, yeah

jim_thompson5910 · Answer

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jim_thompson5910 · Answer

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