2 The amount of stress an IG88 bolt made by MetalCraft can t

2) The amount of stress an IG-88 bolt made by MetalCraft can take before shearing is randomly distributed with a mean of 1500 pounds and a standard deviation of 30 pounds. A competitor, StealWorks has manufactured a bolt that they claim is just as good for a lot cheaper. You purchase 50 of StealWorks new bolts, and test each bolt. The average shear strength was only 1490 pounds. If this had been a sample of MetalCraft bolts (so that you could use the µ=1500 and =30) how often would a batch of 50 bolts have an average of 1490 or less?

Solution

We first get the z score for the critical value. As z = (x - u) sqrt(n) / s, then as          
          
x = critical value =    1490      
u = mean =    1500      
n = sample size =    50      
s = standard deviation =    30      
          
Thus,          
          
z = (x - u) * sqrt(n) / s =    -2.357022604      
          
Thus, using a table/technology, the left tailed area of this is          
          
P(z >   -2.357022604   ) =    0.009211063 [ANSWER, PROBABILITY OF 1490 OR LESS]