#### Objectives

- Students will understand that normal distributions can be used to approximate binomial distributions whenever both np and n(1 – p) are sufficiently large.
- Students will understand that when either np or n(1 – p) is small, the normal distribution probabilities for impossible numbers of successes (less than 0 or greater than n) are unreasonable.
- Students will formulate guidelines to determine what they mean by sufficiently large for good approximations.

#### Vocabulary

- binomial random variable
- mean
- normal random variable
- number of trials,
*n* - probability distribution function
- probability of success,
*p* - standard deviation

#### About the Lesson

This lesson involves examining the general shape of binomial distributions for a variety of values of *n* and *p*.

As a result, students will:

- Compare the shapes of binomial distributions to those of related normal distributions, recognizing the distinction between discrete and continuous random variables.
- Recognize that normal approximations of binomial probabilities become less and less accurate as either
*np*or*n*(1–*p*) falls below 5 (or 10 or 15) by examining the probabilities calculated from the normal distribution for having the "number of successes" be less than 0 or greater than*n*.