The finished inside diameter of a piston ring is normally di

The finished inside diameter of a piston ring is normally distributed with a mean of 10 centimeters and a standard deviation of 0.04 centimeter. What proportion of rings will have inside diameters exceeding 10.010 centimeters Below what value of inside diameter will 15 percentage of the piston rings fall

Solution

A)

We first get the z score for the critical value. As z = (x - u) / s, then as          
          
x = critical value =    10.01      
u = mean =    10      
          
s = standard deviation =    0.04      
          
Thus,          
          
z = (x - u) / s =    0.25      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   0.25   ) =    0.401293674 [ANSWER]

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b)

First, we get the z score from the given left tailed area. As          
          
Left tailed area =    0.15      
          
Then, using table or technology,          
          
z =    -1.036433389      
          
As x = u + z * s,          
          
where          
          
u = mean =    10      
z = the critical z score =    -1.036433389      
s = standard deviation =    0.04      
          
Then          
          
x = critical value =    9.958542664   [ANSWER]