Among diabetics the fasting blood glucose level X may be ass

Among diabetics, the fasting blood glucose level X may be assumed to be approximately normally distributed milligrams (per 100 milliliters) and a standard deviation milligrams(per 100 milliliters). Find the percentage of diabetics who have blood glucose level of 114 milligrams or more. What is the blood glucose level X0 such that for 10% of the diabetics their blood glucose level exceeds X0?

Solution

2a)

We first get the z score for the critical value. As z = (x - u) / s, then as          
          
x = critical value =    114      
u = mean =    106      
          
s = standard deviation =    8      
          
Thus,          
          
z = (x - u) / s =    1      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   1   ) =    0.158655254 [ANSWER]

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2b)

First, we get the z score from the given left tailed area. As          
          
Left tailed area = 1 - 0.10 =   0.9      
          
Then, using table or technology,          
          
z =    1.281551566      
          
As x = u + z * s,          
          
where          
          
u = mean =    106      
z = the critical z score =    1.281551566      
s = standard deviation =    8      
          
Then          
          
x = critical value =    116.2524125   [ANSWER]