A book publisher knows that it takes an average of nine business days from when the material for the book is finalized until the first edition is printed and ready to sell. Suppose the exact amount of time has a standard deviation of four days.

1. Suppose the publisher examines the printing time for a sample of 36 books. What is the probability that the sample mean time is shorter than eight days?
2. Suppose the publisher examines the printing time for a sample of 36 books. What is the probability that the sample mean time is between 7 and 10 days?
3. Suppose the publisher signs a contract for the printer to print 100 books. If the average printing time for 100 books is longer than 9.3 days, the printer must pay a penalty. What is the probability the penalty clause will be activated?
4. Suppose the publisher signs a contract for the printer to print 10 books. If the average printing time for the 10 books is longer than 9.7 days, the printer must pay a penalty. What is the probability the penalty clause will be activated?