answer answer answerSolutiona We first get the z score for t

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answer:

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Solution

a)

We first get the z score for the critical value. As z = (x - u) / s, then as          
          
x = critical value =    60      
u = mean =    75      
          
s = standard deviation =    8.2      
          
Thus,          
          
z = (x - u) / s =    -1.829268293      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   -1.829268293   ) =    0.966320287 [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 =    75      
          
s = standard deviation =    8.2      
          
Thus,          
          
z = (x - u) / s =    -1.219512195      
          
Thus, using a table/technology, the left tailed area of this is          
          
P(z <   -1.219512195   ) =    0.111324925

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c)

We first get the z score for the critical value. As z = (x - u) / s, then as          
          
x = critical value =    31      
u = mean =    75      
          
s = standard deviation =    8.2      
          
Thus,          
          
z = (x - u) / s =    -5.365853659      
          
Thus, using a table/technology, the left tailed area of this is          
          
P(z <   -5.365853659   ) =    4.02836*10^-8

This is a very low probability, which indicates that he is unlikely to be an elite athlete. [ANSWER, NO]