MAT 152 Chapter 5 Lab Objectives: Use Excel to build a probability distribution and find the expected value for the NC POWERBall Lottery and answer questions about the lottery. Use Excel to build a Binomial Probability Distribution and answer questions about it using the distribution and the =BINOM.DIST formula Use Excel to calculate probabilities for a random variable that follows the Poisson Distribution. Directions: POWERBall: The NC POWERBall Lottery is played by picking 5 numbers, from 1 to 69, that you think will match the numbers on 5 balls drawn at random (the order does not matter, the numbers just have to match) AND picking 1 number, from 1 to 26, that matches the "powerball" drawn separately. If all numbers match, you win the Jackpot! (As of this writing, the Jackpot is $60 Million) It costs $2.00 to play. Calculate the probability of winning the Jackpot. (See: Counting Techniques from 4.4) Construct a probability distribution for the random variable, "Winnings." Calculate the expected value for playing POWERBall. o1.) In a text box, interpret this expected value by completing this statement: "Every time you play POWERBall, you should expect to (win/lose) $________ NOTE: This is EVEN IF YOU EVENTUALLY WIN! Theoretically, you would have to play it so many times to win that you still...(see expected value). In the same text box, answer the following questions using Excel: o2.) If the Jackpot increases to $120 Million, what happens to the expected value? (Use specific values) o3.) If the ticket price increases to $4.00, what happens to the expected value? (Use specific values) o4.) If the $2.00 ticket price and the $60 Million Jackpot remain the same, but they change the game to drawing only 3 balls and a power ball, what happens to the expected value? (Use specific values)