Recently my father’s combine auger fell off while he was unloading wheat. What had happened was the ball bearing were rusty, bound up and fell out of the auger. Without these ball bearings the entire auger fell off of the machine. It was impossible to count them because we couldn’t find them all anymore, and so the question became . . . How many ball bearings do I need to order from the parts store in order to have the correct amount. The parts store is a one day drive away, and so we had to have an accurate count before we drove to go get them or we would have lost an entire day, and still could not fix the machine. So here is your problem. All you have is a dollar bill to measure with. You could only find four ball bearings. How many bearing do you need to order to completely cover the outside of the ring so that we can fix the auger?
Several years ago, I went to NCTM in Salt Lake City. A great experience! I saw a presenter use fathom to analyze our chips ahoy chocolate chip counting. It is hard to decide what a chip is in this case, because chips ahoy chocolate chips are just slivers of chocolate. This adds some nice variability to the number of chips, but it just seemed messy both numerically and on my desk.
This year my wife and I baked 4 dozen chocolate chip cookies. I gave each student two cookies and had them count the chips as they ate them. I then had them add this class data in a spreadsheet and find the mean, variance, and standard deviation. I noticed that one student was taking out the chips and giving them to another student to eat. Most noticed the mode and range right away. One cookie had 5 chips and one cookie had 20 chips. The student giving away chips said she wishes she had a cookie with less than 5 chips in it and the other student eating all of the chips wished he had a cookie with more than 20 chips in it.
With that in mind I placed these two questions on the board. If all cookies were placed in a bag, what is the probability of pulling out a cookie with less than 5 chips in it (assuming that the data is normally distributed)? What is the probability of pulling out a cookie with more than 20 chips in it?