Respuesta :
Answer:
The probability that an elite athlete has a maximum oxygen uptake of at least 50 ml/kg is 0.9970.
Step-by-step explanation:
The random variable X can be defined as the amount of oxygen an athlete takes in.
The mean maximum oxygen uptake for elite athletes is, μ = 65 ml/kg.
The standard deviation is, σ = 5.3 ml/kg.
The random variable X is approximately normally distributed.
Now to compute probabilities of a normally distributed random variable, we first need to convert the value of X to a z-score.
[tex]z=\frac{x-\mu}{\sigma}[/tex]
The distribution of these z-scores is known as a Standard normal distribution, i.e. [tex]Z\sim N(0, 1)[/tex].
A normal distribution is a continuous distribution. So, the probability at a point on a normal curve is 0. To compute the exact probabilities we need to apply continuity correction.
Compute the probability that an elite athlete has a maximum oxygen uptake of at least 50 ml/kg as follows:
P (X ≥ 50) = P (X > 50 + 0.50)
= P (X > 50.50)
[tex]=P(\frac{x-\mu}{\sigma}>\frac{50.50-65}{5.3})[/tex]
[tex]=P(Z>-2.74)\\=P(Z<2.74)\\=0.99693\\\approx 0.9970[/tex]
Thus, the probability that an elite athlete has a maximum oxygen uptake of at least 50 ml/kg is 0.9970.
