The American Rifleman (June 1993) reported on the velocity of ammunition fired f

Question

The American Rifleman (June 1993) reported on the velocity of ammunition fired from the FEG P9R pistol. Field tests revealed that Winchester bullets fired from the pistol had an average velocity of 936 feet per second and a standard deviation of 10 feet per second. Tests were also conducted with Uzi and Black Mills ammunition. A bullet whose brand is unknown is fired from the FEG P9R. The velocity of the bullet is 1,000 feet per second. Is the bullet likely to be manufactured by Winchester? Explain you answer. Assume a normal distribution.

Explanation / Answer

We first get the z score for the critical value. As z = (x - u) / s, then as          
          
x = critical value =    1000      
u = mean =    936      
          
s = standard deviation =    10      
          
Thus,          
          
z = (x - u) / s =    6.4      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   6.4   ) =    7.76885*10^-11

Hence, as the probability is so small, (P<0.05) then IT IS UNLIKELY TO BE MANUFACTURED BY WINCHESTER.

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