Fun with Probability! The Probable Pen in the Cereal Box Final Results as of June 11, 1996

Whew! After a grueling end-of-semester, I have included all of the submissions that trickled in after the closing date. Our final solution included 2198 students. We have collectively purchased 34,313 boxes of cereal! That's nearly $100,000 worth of cereal. Click here to see the final submission list. Also, see the comments page. Also, a graph of pen distribution.

• Max: 95 We found you Carrie! (Columbia, MO) Your question is answered.
• Min: 6 (43 Students)
• Median: 14.00
• Mean: 15.61 - Note this is almost a full unit above the expected value of 14.7. I'm not sure why. Perhaps the model of using a six-sided die is not quite accurate? You would think with 33,000+ rolls we would get closer... As an exercise, I have graphed the Mean and Standard Deviation over the life of the project.
• StDev: 7.51
• Count (Students): 2198 (Represents 34,313 die rolls)

And our latest histogram (this shows the distribution of rolls for the 47 reporting classes):

Don't forget to check out the registrant information (it even has some 3-D graphs!). Also, for a history of results pages, check out the results index.

We now have a new graph. The following bar chart shows the distribution of pens by color. Notice that each pen is (approximately) equally likely to be found in the cereal box.

And now a history of the mean and standard deviation:

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