Over many years a library has found it checks out an average of 320 books per day, with a standard deviation of 75 books per day. Consider that the number of books checked out per day is normally distributed. Find the probability (to 4 decimal places) that:

a) less than 200 books per day are checked out.( )

b) if a sample of 35 days is selected, that this sample mean will be between 310 and 340 books per day.( )