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? (b) What is the probability that an elite athlete has a maximum oxygen uptake of 7070 ml/kg or lower? (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."

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

introduction, methodology, results, discussion

step-by-step explanation:

an observational study is one which consists of actual observation to record data and then analyse the data.

there are a number of factors that should be analyzed before starting an observational study.

the main four factors are:

i) introduction:   this should be analysed to check whether the purpose of the study is correctly established and the data recorded are appropriate for the study

methodology:   the method of collecting the data, such as whether randomly selected, and whether sample size matches with the population to be studied, whether questions asked are easy to answer by common men, etc.

results: then results such as summary of data with comments should be studied thoroughly

discussion:   the last is the discussion, this can be either by management people or persons who are all interested , etc.