Follow the instructions and answer the questions.
Have you ever wondered how long coins stay in circulation? Are you a collector? Get a wrapper of pennies
(that contains $0.50). Your first task is to form a distribution of their ages.

1. Organize the data by using a stemplot of the ages. Split the stems to give a sufficient number of stems to the
data (recall, splitting the stems means that you have 2 stems for each value, one with values 0-4 and the second
with 5-9). You must have between 5 and 20 stems.

2. What is the shape of the distribution? Why do you think it is this shape?

3. Find the five-number summary for this data set.

4. Using the five-number summary and the definition of an outlier, do you find any outliers? By using the
definition of outlier and the five-number summary, what is the age of a “rare” coin?

5. Do you think the distribution of all pennies in circulation is similar to your sample?

6. List the characteristic assumptions for the Central Limit Theorem and decide if they are satisfied by your
distribution.

7. Find the mean and standard deviation of the ages of the pennies in your sample.
Mean = _____ SD = _____ n = _____

8. Compute a 95% confidence interval for the mean ages of pennies.

9. What is the margin of error for your estimate?

10. 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. Determine the sample size you would need for a one-year margin of error with
99% confidence.

11. By using the normal curve, the mean, and the standard deviation of your sample, find the age that you
would begin to save before the pennies become hard to find. Consider the coin “rare” if the age is the oldest 2%
or less of the population.

12. Consider your roll of pennies as a population (so you know the population mean and standard deviation
from #7 above). Use the scale of ages on the number line below and plot µ. 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, µ. Draw a line segment for this interval below the number line that you have scaled. Mix up the pennies
and repeat the process five times. Do the intervals of your sample capture the value of µ? Why?

5 10 15 20 25 30 35 40 45 50 55
Plot #1
Plot #2
Plot #3
Plot #4
Plot #5

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