AP Statistics / Mr. Hansen

Name: _________________________________

3.

In most large-scale standardized exams, the students’ scores will be normally distributed. (In fact, if you ever go into teaching, you will discover that even most "homegrown" tests and quizzes produce normally distributed results. It’s amazing!) However, the state of Tennehoovia has administered a high school competency exam that shows the following counts of students in each score range of size 10: 25, 350, 3542, 6199, 7208, 13572, 8192, 3150, 2588, 2120. For example, 25 students scored below 10% on the exam, 350 scored greater than or equal to 10% but less than 20%, 7542 scored greater than or equal to 20% but less than 30%, and so on. If the Tennehoovia student scores have a mean score of 54.624% and standard deviation 18.4%, are they consistent with a normal distribution?

4.

An upcoming 3-way election between Tweety, Sylvester, and the Tasmanian Devil ("Taz") is considered to be neck-and-neck. In fact, the latest poll showed virtually a dead heat, with the margin of error being too large to predict a clear winner. As fans of Taz, we would like to design a new survey that reduces the margin of error to no more than 1/3 of a percentage point so as to improve our ability to predict whether Taz will win. How many people must we poll? (Remember that polling is quite expensive.) Give both a conservative answer and a more aggressive answer that saves money.

5.

On a trip to Las Vegas, the Hughleys noticed that the roulette wheel (which should come up black or red equally often) came up red on 52 out of 75 spins. Is there evidence that the wheel is rigged? Answer this question two ways, once using z procedures and once using c² procedures.