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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]

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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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