The distribution of the ages, not the year the coin was minted, will be examined. The central limit theorem will be used to form an interval estimation of the ages for your sample of coins.
One roll of pennies.
Have you ever wondered how long coins stay in circulation? Are you a collector? You are to go to a bank and get a roll of pennies. Your first task is to form a distribution of their ages (NOT the year on the coin).
1.Organize the data by using a stemplot of the ages. If you use CrunchIt to develop your stemplot, right click and drag to highlight the stemplot, copy and paste it into here.
2. What is the shape of the distribution? Why do you think it is this shape? Did you find any outliers?
3. Do you think the distribution of all pennies in circulation is similar to your sample? Explain your answer.
4. Find the mean and standard deviation of the ages of the pennies in your sample.
5.Compute a 95% confidence interval for the mean ages of pennies.
6. What is the margin of error for your estimate?
7.The president of “COINS UNLIMITED” has just hired you as his chief statistician for his research on the age of pennies. You are charged with the task of estimating the average age of pennies in circulation within one year of age with 99% confidence. How large of a sample would you need to obtain? Use the standard deviation from your sample as your best estimate of the population standard deviation. (See formula on page 405). Show your work.
8. Consider your roll of pennies as a population. Choose 20 pennies at random from your pile of pennies. Find the mean and standard deviation of the sample and compute a 95% confidence interval for the population mean, u. Mix up the pennies and repeat the process 2 times