On the following problem I need to understand how the follow

Solution

a)

We first get the z score for the critical value. As z = (x - u) / s, then as          
          
x = critical value =    90000      
u = mean =    85900      
          
s = standard deviation =    11000      
          
Thus,          
          
z = (x - u) / s =    0.372727273      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   0.372727273   ) =    0.354675718 [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 =    75000      
u = mean =    85900      
          
s = standard deviation =    11000      
          
Thus,          
          
z = (x - u) / s =    -0.990909091      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   -0.990909091   ) =    0.839135014 [ANSWER]

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You may be speaking of part A. In that case, maybe your professor is using a table representing areas between the mean to the z score. Note that the area to the right of the mean is 0.5000. Meanwhile, he seemed to round off z to 2 decimal places, so he got the area of 0.1443. Then, to get the area to the right of that z score, he subtracted it to 0.5000.