Suppose cracks exist in a certain material and the crack len
     Suppose cracks exist in a certain material, and the crack length [in micrometers (mum)] of a randomly selected crack is normally distributed with an average length of 71 nm and a variance of 6.25 (mum)^2.  What percentage of cracks are over 74 mum long?  Determine the 90-percentile value of the crack length, i.e., the crack length which has a 90% probability of not being exceeded.  What percentage of cracks exceeding 72 mum are over 77 mum?![Suppose cracks exist in a certain material, and the crack length [in micrometers (mum)] of a randomly selected crack is normally distributed with an average le  Suppose cracks exist in a certain material, and the crack length [in micrometers (mum)] of a randomly selected crack is normally distributed with an average le](/WebImages/10/suppose-cracks-exist-in-a-certain-material-and-the-crack-len-1005433-1761518270-0.webp) 
  
  Solution
![Suppose cracks exist in a certain material, and the crack length [in micrometers (mum)] of a randomly selected crack is normally distributed with an average le  Suppose cracks exist in a certain material, and the crack length [in micrometers (mum)] of a randomly selected crack is normally distributed with an average le](/WebImages/10/suppose-cracks-exist-in-a-certain-material-and-the-crack-len-1005433-1761518270-0.webp)
