Your lumber company has bought a machine that automatically cuts lumber.  The seller of the machine claims that the machine cuts lumber to a mean length of 8 feet (96 inches) with a standard deviation of 0.5 inch.  Assume the lengths are normally distributed.  You randomly select 40 boards and find that the mean length is 96.25 inches.

1. Assuming that the seller's claim is correct, what is the probability the mean of the sample is 96.25 inches or more? {#1}
   
   
2. Using your answer from question 1, what do you think of the seller's claim?
   {#2}
   
   
3. Would it be unusual to have an individual board with a length of 96.25 inches?  Why or why not?
   {#3}