The average library patron reads 42 books each year, with a standard deviation of 10 books. The library would like to reward its top 25% of patrons, as judged by the number of books read each year.

Use a calculator to find how many books must a library patron read to be eligible for the reward if the library is only examining 100 patrons.

Round x¯ and σx¯ up to the nearest whole number.