#### 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?

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.

• Binary: Each trial is either a success or failure.
• Independent: Each trial is independent. So knowing the outcome of one trial tells us nothing about the outcomes of the other trials.
• Number of trials is fixed (n).
• Success. 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.
•  In the BINS acronym, the S can also stand for Same probability of success.
• 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.