The physical fitness of an athlete is often measured by how much oxygen the athl

Question

The physical fitness of an athlete is often measured by how much oxygen the athlete takes in (which is recorded in milliliters per kilogram, ml/kg). The mean maximum oxygen uptake for elite athletes has been found to be 75 with a standard deviation of 9.3. Assume that the distribution is approximately normal. (a) What is the probability that an elite athlete has a maximum oxygen uptake of at least 55 ml/kg? (b) What is the probability that an elite athlete has a maximum oxygen uptake of 70 ml/kg or lower? (c) Consider someone with a maximum oxygen uptake of 30 ml/kg. Is it likely that this person is an elite athlete? Write "YES" or "NO".

Explanation / Answer

= 75, = 9.3

(a) z = (55 - 75)/9.3 = -2.1505

P(x 55) = P(z > -2.1505) = 0.9842

(b) z = (70 - 75)/9.3 = -0.5376

P(x 70) = P(z < -0.5376) = 0.2954

(c) z = (30 - 75)/9.3 = -4.8387

It is unlikely that this person is an elite athlete.

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