The physical fitness of an athlete is often measured by how much oxygen the athl
ID: 3132399 • Letter: T
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 65 with a standard deviation of 10. Assume that the distribution is approximately normal.
(a) What is the probability that an elite athlete has a maxi- mum oxygen uptake of at least 55 ml/kg?
answer:
(b) What is the probability that an elite athlete has a maxi- mum oxygen uptake of 65 ml/kg or lower?
answer:
(c) Consider someone with a maximum oxygen uptake of 31 ml/kg. Is it likely that this person is an elite athlete? Write ”YES” or ”NO.”
answer:
Explanation / Answer
A)
We first get the z score for the critical value. As z = (x - u) / s, then as
x = critical value = 55
u = mean = 65
s = standard deviation = 10
Thus,
z = (x - u) / s = -1
Thus, using a table/technology, the right tailed area of this is
P(z > -1 ) = 0.841344746 [ANSWER]
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b)
We first get the z score for the critical value. As z = (x - u) / s, then as
x = critical value = 65
u = mean = 65
s = standard deviation = 10
Thus,
z = (x - u) / s = 0
Thus, using a table/technology, the left tailed area of this is
P(z < 0 ) = 0.5 [ANSWER]
*************************
c)
If he's an elite athlete, then the probability that he follows the said distribution is
We first get the z score for the critical value. As z = (x - u) / s, then as
x = critical value = 31
u = mean = 65
s = standard deviation = 10
Thus,
z = (x - u) / s = -3.4
Thus, using a table/technology, the left tailed area of this is
P(z < -3.4 ) = 0.000336929
As this is a very small probability, then NO. [ANSWER: NO]
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