Statistics 3 - The Toothpick Box

Every year when we get into the statistics part of precal, i ask the students:

"so how many toothpicks do you think there are in a box of toothpicks that says 250 Toothpicks" ?

Almost all the students yell 250 !! (of course, it says so on the box)

So now we make a few coke bets (diet coke for ME) and we send a responsible senior to the nearby grocery store to buy a box of 250 toothpicks.

Remember the movie Rainman ? with Tom Cruise and Dustin Hoffman ? Dustin Hoffman is autistic and Tom sells cars in LA. There father dies and Tom goes back for the reading of the will. The father leaves all the money to his older brother Dustin who is living in a special home.

Tom tries to take Dustin back to LA, but runs into all kinds of problems. One of them is that Dustin will NOT fly. Another is that Dustin has to see Judge Wabber every night at 7 pm on TV.

They are in a Diner, when the waitress drops a box of toothpicks and Dustin says "246". Tom says 246 what ? and Dustin says 246 again.

Tom looks at the toothpick box in the waitress hand and there are only 4 toothpicks left in the box, and the box says 250 on the cover. That means there are 246 toothpicks on the floor and Dustin somehow counted them as the fell or once they were on the floor. Autistic.

So Tom gets this great idea that Dustin can count cards, and they go to Vegas.

So again i ask the class:
"how many toothpicks are there in a box of 250 toothpicks" ?

And they all yell, 250 !!

When the responsible senior comes back we sit down and count the toothpicks. I have done this for over 30 years and sometimes with 2 or 3 classes a year.

WE HAVE NEVER COUNTED EXACTLY 250 TOOTHPICKS !!

We have actually gone over 250 only two times....the lowest i can remember was below 240.

You see a machine can NOT count exactly 250 toothpicks....for a machine to do that it would cost way too much (only machines that work with the space program are that accurate).

My data has shown a mean (average) of 246 and a standard deviation (SD) of 3. That means we should expect that 95% of the boxes should have between 252 and 240 toothpicks in them. (mean plus or minus 2 SD's)

It is strange that we have never gotten 250 exactly.