answer answerSolutiona We first get the z score for the crit

answer:

answer:

Solution

a)

We first get the z score for the critical value. As z = (x - u) / s, then as          
          
x = critical value =    70      
u = mean =    74      
          
s = standard deviation =    9.3      
          
Thus,          
          
z = (x - u) / s =    -0.430107527      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   -0.430107527   ) =    0.666441287 [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 =    76      
u = mean =    74      
          
s = standard deviation =    9.3      
          
Thus,          
          
z = (x - u) / s =    0.215053763      
          
Thus, using a table/technology, the left tailed area of this is          
          
P(z <   0.215053763   ) =    0.585137299 [ANSWER]

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c)

This means getting a z score from -3 to 3.

z1 = lower z score =    -3      
z2 = upper z score =     3      
          
Using table/technology, the left tailed areas between these z scores is          
          
P(z < z1) =    0.001349898      
P(z < z2) =    0.998650102      
          
Thus, the area between them, by subtracting these areas, is          
          
P(z1 < z < z2) =    0.997300204   [ANSWER]