1. A new employee is supposed to be sorting coated lenses into one of three bins: ship, rework, or scrap. However, this employee was not well trained and sorts 50 lenses by randomly putting each lens in one of the three bins.
(a) Let Y be the number of lenses the employee sorts correctly. What is the distribution of Y?
(b) Find P(Y 10).
(c) Find E(Y ).
(d) Find Var(Y).
2. The new employee from the previous problem was retrained and put back to work sorting lenses into three bins: ship, rework, and scrap. A well-trained worker will sort with 98% accuracy. To check to see if the new employee was now well trained a supervisor re-checked 50 lenses sorted by the new employee. If the employee is now well trained, how many lenses would the supervisor expect to find sorted incorrectly?