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12 December, 14:49

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:

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  1. 12 December, 15:08
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    Step-by-step 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
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