Suppose a quiz has 9 multiple choice questions. Each question has 5 answer choices. If a student takes the quiz and randomly guesses on every question.

Question 1: Find the probability the student gets between 2 and 7, exclusive, questions correct.

Question 2: Find the probability the student gets more than 5 questions correct.

One state lottery has 900 prizes of $1; 140 prizes of $10; 20 prizes of $50; 5 prizes of $365; 2 prizes of $1,070; and 1 prize of $2,800. Assume that 27,000 lottery tickets are issued and sold for $1.

Question 3 What is the lottery's expected profit per tickets?

Question 4 What is the lottery's standard deviation of profit per ticket?