MATH318: Binomial Probability Distribution

What is a binomial distribution?  When is it OK to apply the formulae for binomial distributions to the data you have?  What do the formulae predict for a given set of data?  This worksheet was designed to explore these questions.

Carefully read the start of Section 3.3 (about one page, starting on page 69). You may also wish to browse the remainder of Section 3.3. Then answer the questions below, referring to section 3.3 as necessary.

This worksheet has been revised to raise awareness of Arizona's ban on Mexican American studies in high school, using statistics from the Huffington Post.

Research shows that 34.3 percent of Hispanic teenagers in the US said they were bullied in the classroom, compared to 31.3 percent of white students who reported being bullied in school.

  1. (20 pts) Suppose the experiences (bullied or not bullied) of a class of 20 Hispanic teenagers represent 20 trials in a binomial experiment (see page 69). We will say that a trial (represented by surveying one teenager) is a failure if a student reports bullying; otherwise it is a success.

    In this context, what is the random variable x described on page 69?




  2. (20 pts) At the bottom of page 69 is a list of conditions an experiment must satisfy in order for the formulae in this section to give accurate predictions.  For each condition, discuss whether the experiment "survey a class of 20 Hispanic teenagers in a randomly selected US high school" satisfies that condition.
    1. The experient consists of a sequence of n identical trials. (If so, what is n?)



    2. Two outcomes are possible on each trial -- success and failure.





    3. The probabilities of the two outcomes do not change from one trial to the next.





    4. The trials are independent -- the outcome of one trial does not affect the outcome of any other trial.





  3. (10 pts)  There is a 34.3% chance of an Hispanic teenager being bullied in class. What is the chance p of success in one trial, when success is defined as in problem 1?


  5. (15 pts) If this is a true binomial experiment, what is f(15)? In other words, in a class of 20 Hispanic teenagers, what is the probability that 5 report classroom bullying and 15 do not? (You can use the Excel FACT function to compute 15!.)




  6. (20 pts) In a class of 20 Hispanic teenagers, what is the probability that none of the students report bullying?  Is this outcome likely?





  7. (15 pts) In a class of 20 Hispanic teenagers, what is the probability that at least two report bullying?








Bonus: (5 pts) In a group of 100 Hispanic teenagers, what is the probability that more than 34 report bullying? Justify your answer.