In this lesson, students will discover that a binomial distribution can be closely modeled by a normal distribution, under certain conditions. At this point in the school year, these normal distribution calculations should be almost automatic (we did this in Chapter 2 and again in Lesson 6.1).

 

You might have some savvy students worried in question #1 about the independent condition because we are sampling without replacement. Have them consider how much probabilities change when 1 green Skittle is removed. 240/1200 = 0.2000 versus 239/1199 = 0.1993. Because these probabilities are almost exactly the same, we are willing to let this issue slide (see 10% condition discussion below). 

 

Formalize Later

When debriefing question #1 in the activity, make students aware that the Independent condition is not perfectly met, but that we are willing to let this go because the probabilities change so little when sampling without replacement. The reason is because the sample size is so small relative to the population size. In some courses (including AP Stats), students use the 10% condition (the sample size is less than 10% of the population size) as a rule for determining if the Independent condition is close enough. For Intro Stats, we make note of this in the debrief but we do not carry this forward as a necessary condition to check when we get to inference. 

 

When debriefing question #3 in the activity, you will want to introduce the Large Counts condition. Rather than just telling students to check np and n(1 – p) are both greater than 10, we suggest trying to motivate some of this thinking using this Normal Approximation to Binomial Distributions applet.