top of page

## Chapter 6 - Day 7 - Lesson 6.3

##### 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.

##### Archived Activity: Will EKHS Girls Soccer 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.

bottom of page