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 70 with a standard deviation of 6.5. Assume that the distribution is approximately normal.

A. What is the probability that an athlete has a maximum oxygen uptake of at least 50 ml/kg?

B. What is the probability that an athlete has a maximum oxygen uptake of 70 ml/kg or lower?

C. Consider someone with a maximum oxygen uptake of 35 ml/kg. Is it likely that is person is an elite athlete?

Answer 1

Let X is a random variable shows the maximum oxygen uptake for elite athletes. Here X has normal distribution with following parameters:

A:

The z-score for X = 50 is

The probability that an athlete has a maximum oxygen uptake of at least 50 ml/kg is

B:

The z-score for X = 70 is

The probability that an athlete has a maximum oxygen uptake of 70 ml/kg or lower is

C:

The z-score for X = 35 is

The probability that an athlete has a maximum oxygen uptake of 35 ml/kg or lower is

Since this probability is less than 0.05 so it is not usual event. It is not likely that is person is an elite athlete.