Carefully read the start of Section 3.3 (about one page, starting on page 65). 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 6 Hispanic teenagers represent 6 trials in a binomial experiment (see page 66). 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 66?

    

    

    

2. (15 pts) At the bottom of page 65 is a list of conditions an experiment must satisfy in order for the formulae in this section to give accurate predictions.  Circle any groups below which satisfy these conditions and briefly explain your selection.

   Six siblings, aged 13-19.

   Six students picketing the Arizona State House.

   Six students selected at random from a Tuscon high school.

   Six responses selected at random from a nationwide survey of Hispanic teenagers.

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?

 

4. (15 pts) If this is a true binomial experiment with 6 trials, what is f(4)? In other words, in a group of 6 randomly selected Hispanic teenagers, what is the probability that 2 report classroom bullying and 4 do not?

    

    

    

5. (20 pts) In a randomly selected group of 6 Hispanic teenagers, what is the probability that none of the students report bullying?  Is this outcome likely?

    

    

    

6. (20 pts) In a group of 6 Hispanic teenagers, what is the probability that at least two report bullying? (Hint: there are two ways of doing this problem. The faster way uses complementary probabilities.)