# 17 Lab 4: Part 2 - The Binomial Distribution

### 17.0.1 Introduction

This lab was adapted from the following lab which was given as part of a 2009 version of STAT 10 at UCLA.

http://www.stat.ucla.edu/~yexy/stat10/lab3.pdf

For this lab we will continue thinking about the imbalance between male and female births in the USA.

The tutorial contained a link to a news article which had some information we needed for our simulation. The article is linked again below because you will need to dig through its contents (including links inside of the article) in order to correctly complete tasks for this lab.

**Please do not use any other sources of information.** It may be tempting to just Google information that you might be able to use to answer the first question instead of doing the hard work of finding this stuff inside of the provided source. However, there is no guarantee that alternative sources will contain the same information that will be used to evaluate your work. This means that if you use the wrong data to do your calculations, your errors will cascade through your work and add up to a lot of lost points. Please follow the instructions as they are written!

### 17.0.2 Your tasks

- Calculate the percentage of births in the USA that were female for the year that you were born. If you cannot find information for the year of your birth, use information for the most recent year that is available. Calculate this number inside of your lab report, save it as a variable so that you can use it later and print it so that its accuracy can be easily verified. Please do not round the number.

- Hint: Completion of the above task will require some detective work. This part of the lab is very important! If you get this wrong, it will throw off the rest of your calculations!

Using the value you calculated in the last problem together with R’s built-in functions for the binomial distribution, calculate the theoretical probabilities for the possible numbers of girls that a family with three children could have. Store this information in a dataframe that is easy to read and print it inside of your lab report.

Using the same probability that was calculated in Question 1 together with a

`seed`

integer of 10, simulate outcomes for 10 families. Add this simulated data to the dataframe you created for your answer to Question 2. Print your results inside of your lab report.Repeat what you did to answer Question 3 for 1,000 families. Print your results inside of your lab report.

Explain why your empirical results are not exactly equal to the theoretical probabilities.