**Learning Targets**

**Determine whether the conditions for a binomial setting are met.****Calculate the mean and standard deviation of a binomial random variable. Interpret these values in context.**

Quick Lesson Plan |
Time |

Activity | 15 minutes |

Debrief Activity | 10 minutes |

Big Ideas | 5 minutes |

Check Your Understanding | 10 minutes |

Bonus Time | 20 minutes |

**Activity: Will the EKHS girls’ soccer team win? **

**Download Word | pdf | Answer Key **

The Mathalicious activity from yesterday was long and we didn’t get too much time to discuss the conditions necessary for a binomial distribution (BINS), so we focus in on that learning target for a second day today.

Also by the end of this activity, we want to introduce students to the formulas for mean and standard deviation for a binomial distribution. Instead of just giving students these formulas, we allow them to calculate mean and standard deviation for a random variable the long way (as learned in Section 6.1). In the Debrief, we reveal to them that there are in fact nice formulas to do this calculation.

**BINS!**

To help students remember the four conditions necessary for a binomial distribution, we use the acronym BINS.

**B**inary: Each trial is either a success or failure.**I**ndependent: Each trial is independent. So knowing the outcome of one trial tells us nothing about the outcomes of the other trials.**N**umber of trials is fixed (n).**S**uccess. The probability of success for each trial is the same (p).

**Teaching tips for BINS!**

- The term “trials” can be used interchangeably with the term “observations.”
- Tell students that a “success” does not always mean something awesome happened. A “success” could be defined as a faulty part or a person being diabetic.
- On many AP Exam questions involving binomial settings, students do not recognize that using a binomial distribution is appropriate. In fact, free-response questions about the binomial distribution are often among the lowest-scoring questions on the exam. Make sure to spend plenty of time learning how to identify a binomial distribution.