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 8080 with a standard deviation of 5.85.8. Assume that the distribution is approximately normal. (a) What is the probability that an elite athlete has a maximum oxygen uptake of at least 6565 ml/kg? answer: (b) What is the probability that an elite athlete has a maximum oxygen uptake of 7070 ml/kg or lower? answer: (c) Consider someone with a maximum oxygen uptake of 3030 ml/kg. Is it likely that this person is an elite athlete? Write "YES" or "NO." answer:

Answer 1

Explanation:

we would apply the formula for normal distribution which is expressed as

z = (x - µ)/σ

Where

x = maximum oxygen uptake for elite athletes.

µ = mean maximum oxygen uptake for elite athletes

σ = standard deviation

From the information given,

µ = 80

σ = 5.8

1)

the probability that an elite athlete has a maximum oxygen uptake of at least 65 ml/kg is expressed as

P(x ≥ 65) = 1 - P(x < 65)

For x = 65

z = (65 - 80)/5.8 = - 2.59

Looking at the normal distribution table, the probability corresponding to the z score is 0.0048

P(x ≥ 65) = 1 - 0.0048 = 0.9952

2)

the probability that an elite athlete has a maximum oxygen uptake of 70 ml/kg or lower is expressed as

P(x ≤ 70)

For x = 70,

z = (70 - 80)/5.8 = - 1.72

Looking at the normal distribution table, the probability corresponding to the z score is 0.043

P(x ≤ 70) = 0.43

3)

For someone with a maximum oxygen uptake of 3030 ml/kg,

z = (30 - 80)/5.8 = - 8.62

Probability = 0.00015

The probability of an elite athlete having a maximum oxygen uptake of 30 ml/kg is very low. Thus the answer is NO