Can you please assist The physical fitness of an athlete is often measured by how much oxygen the athlete takes in (which isrecorded in milliliters per kilogram, ml/kg). The mean maximum oxygen uptake for elite athletes has beenfound to be 69 with a standard deviation of 7.4. Assume that the distribution is approximately normal.Find the probability that an elite athlete has a maximum oxygen uptake of at least 84.54 ml/kg.Find the probability that an elite athlete has a maximum oxygen uptake of at most 53.46 ml/kg.Find the probability that an elite athlete has a maximum oxygen uptake of 53.46 ml/kg.

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Description: Can you please assist The physical fitness of an athlete is often measured by how much oxygen the athlete takes in (which isrecorded in milliliters per kilogram, ml/kg). The mean maximum oxygen uptake for elite athletes has beenfound to be 69 with a

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

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Can you please assist

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 69 with a standard deviation of 7.4. Assume that the distribution is approximately normal.
Find the probability that an elite athlete has a maximum oxygen uptake of at least 84.54 ml/kg.
Find the probability that an elite athlete has a maximum oxygen uptake of at most 53.46 ml/kg.
Find the probability that an elite athlete has a maximum oxygen uptake of 53.46 ml/kg.

Expert Solution

Step 1

Given Information:

Mean $μ = 69$

Standard deviation $σ = 7.4$

Let X denote the amount of oxygen uptake for elite athletes.

a) To find the probability that an elite athlete has a maximum oxygen uptake of at least 84.54 ml/kg:

z-score is a measure which indicates how many standard deviations away, a data value is, from the mean. It is given by the formula:

$z = \frac{X - μ}{σ}$

Required probability is obtained as follows:

$\begin{array}{rcl} P (X \geq 84.54) & = & P (\frac{X - μ}{σ} \geq \frac{84.54 - 69}{7.4}) \\ = & P (z \geq 2.1) \\ = & 1 - P (z < 2.1) \\ = & 1 - 0.98214 [u \sin g s \tan d a r d n o r m a l t a b l e] \\ = & 0.01786 \end{array}$

Thus, the probability that an elite athlete has a maximum oxygen uptake of at least 84.54 ml/kg is 0.0179

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