## ALGII.7 Statistical Inferences

### Driving Question

When should NFL teams go for it on fourth down? Students use quadratic functions to develop a model of expected points. They then apply this model to determine when teams should punt the ball, and more importantly, when they shouldnâ€™t.

Topic: Building Functions (BF), Interpreting Functions (IF), Using Probability to Make Decisions (MD)

### Middle Lessons

In basketball, which shot should you take? Students use probability and expected value to determine how much 3-point and 2-point shots are really "worth" to different NBA players.

Topic: Conditional Probability and the Rules of Probability (CP)

### Happy Meal

How much should you spend to get all the toys? Students use probability and expected value to figure out how many Happy Meals they should plan on buying if they want to collect all the toys in a series.

Topic: Interpreting Categorical and Quantitative Data (ID), Making Inferences and Justifying Conclusions (IC), Statistics and Probability (SP), Using Probability to Make Decisions (MD)

### The Waiting Game

How many people should you date before you settle down? Students use modeling with probability distributions to come up with a rule to try to maximize their relationship happiness.

Topic: Conditional Probability and the Rules of Probability (CP), Making Inferences and Justifying Conclusions (IC)

### Shuffle

What does it mean for a playlist to be "random?" Students use probability to explore the idea of randomness, as well as the patterns that can emerge from random processes like shuffles.

Topic: Conditional Probability and the Rules of Probability (CP), Interpreting Categorical and Quantitative Data (ID)