SOLUTION: The weights of certain machine componets are normally distrubited with a mean of 8.75g and a standard deviation of 0.07g. Find the two weights that seperate the top 3% and the bott

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Question 103808: The weights of certain machine componets are normally distrubited with a mean of 8.75g and a standard deviation of 0.07g. Find the two weights that seperate the top 3% and the bottom 3%. These weights could serve as limit used to identify which componets should be rejected.
Answer by stanbon(75887) (Show Source):
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The weights of certain machine componets are normally distrubited with a mean of 8.75g and a standard deviation of 0.07g. Find the two weights that seperate the top 3% and the bottom 3%. These weights could serve as limit used to identify which componets should be rejected.
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Use your z-chart or your calculator to find the "z" value that separates the top 3% and the bottom 3%.
That value is z= 1.88 and z=-1.88
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Then find the weights that correspond to those z values:
Let the weight be "x":
z = (x-mu)/sigma
1.88 = (x-8.75)/0.07
x= 0.07*1.88+8.75
x = 8.8816 lbs is the weight that separates the top 3%.
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-1.88 = (x-mu)/sigma
x = 0.07(-1.88)+8.75
x = 8.6184 lbs is the weight that separates the bottom 3%
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Cheers,
Stan H.