A rock band is going to give a concert in your town. To estimate the number of students from your school attending the concert, your principal asks 45 students, chosen at random, whether they plan to attend. Assume that each student has a 65% probability of saying that he or she will attend.
1. You want to use your calculator to conduct a binomial experiment to represent the principal’s survey. Write a calculator statement you can use to carry out one trial. How many trials make up the experiment?
2. Use your calculator to conduct the experiment 20 times. Record the number of successes for each of the 20 times.
3. Because you conducted the experiment 20 times, the experimental probability of k successes is the number of times k successes occurred divided by 20. Construct a histogram showing the probability distribution for your experimental results.
4. Construct a histogram of the binomial distribution for your principal’s survey. These probabilities are the theoretical probabilities.
5. Compare the histograms in Exercises 3 and 4. Discuss the results.
6. Create a situation for which you could conduct a binomial experiment. Conduct the experiment a sufficient number of times so that you feel your results provide a useful prediction of an outcome.
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