1) Suppose a quiz has 11 multiple choice questions. Each question has 5 answer choices. If a student takes the quiz and randomly guesses on every question...

a) Find the probability the student gets between 3 and 8, exclusive, questions correct.

b) Find the probability the student gets more than 7 questions correct.

2) One state lottery has 900 prizes of $1,140 prizes of $10, 25 prices of $55, 5 prices of $360, 2 prizes of $1,090, and 1 prize of $2,400. Assume that 30,000 lottery tickets are issued and sold for $1.

a) What is the lottery's expected profit per ticket?

b) What is the lottery's standard deviation of profit per ticket?