1. Warm Up
A manufacturer of bowling balls produces a ball with a mean weight of 9 pounds and a standard deviation of 0.2 pounds. The bowling balls are shipped in boxes of 12 each. 1) Find the mean weight for a box of bowling balls. 2) Find the standard deviation of the weight of a box of bowling balls.

2. Example
The following is data on SAT scores from 2014: Math Mean = 513 Std Dev = 110 Verbal Mean = 497 Std Dev = 95 1) Find the mean combined (Math and Verbal) SAT score. 2) Find the standard deviation of the combined (Math and Verbal) SAT score.

3. Practice
The concession stand at the theater sells popcorn and soda. The probability distribution for the number of popcorn boxes and sodas a customer orders is shown below. Popcorn Probability Soda Probability ) Find the mean number of items a customer orders. 2) Find the standard deviation of the number of items a customer orders.

4. Example
A manufacturer of bowling balls produces a ball with a mean weight of 9 pounds and a standard deviation of 0.2 pounds. The bowling balls are shipped in boxes of 12 each. Assume the weights of the bowling balls are normally distributed and independent. The shipping company will only accept boxes of less than 110 pounds. What is the probability that some of the company’s boxes will be over 110 pounds?

5. Practice #1
Tom and George bowl together. Assume their scores are independent and both follow a normal distribution. Mean Std Dev Tom George ) Find the mean of the difference in their scores (Tom’s score – George’s score). 2) Find the standard deviation of the difference in their scores. 3) What is the probability George will beat Tom?

6. Practice #2
Previously we found the following data for the heights of men and women in inches. Assume both distributions are normal and independent. Mean Std Dev Men Women Imagine a group of men and women are speed dating, where men and women are paired together for a 5 minute “date” before moving on to another partner. What is the probability the man is shorter than the woman in a randomly selected speed date?

7. Activity – Fantasy Football
Fantasy football has been popular for years. The idea of the game is you pick a “team” of players and, based on the actual games that week, see how many “points” your team scores. You can play against an individual or in a tournament against many teams at once. We will consider a simplified version of fantasy football today. You will pick a team consisting of: 1 Quarterback 1 Running Back 1 Receiver

8. Activity – Fantasy Football
Fantasy football games come in many versions. We will consider a multi-player game (30-60 players) where the team with the most points wins and all other teams lose. Assume from past experience it usually takes 35 points to win one of these games. Players earn points by gaining yards and scoring touchdowns in their actual games. They lose points for interceptions and fumbles. Choose a team from the options on the next slide that gives you the best chance of winning this multi-player game.

9. Activity – Fantasy Football
Quarterback Mean SD Running Back Mean SD Carson Wentz Kareem Hunt Russell Wilson Todd Gurley Drew Brees Ezekiel Elliott Receiver Mean SD Choose 1 of each type. Antonio Brown Assume all players have a Julio Jones normal distribution for T.Y. Hilton points and points are independent. Which team has the best chance to score at least 35 points so you can win in fantasy football?