Determine whether the conditions for a binomial setting are met.
Calculate the mean and standard deviation of a binomial random variable. Interpret these values.
Activity: Pop quiz!
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.
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.
Luke's Lesson Notes
Here is a brief video highlighting some key information to help you prepare to teach this lesson.