You've probably noticed the warning signs in elevators that say something like "Maximum Weight: 1000 pounds", or words to that effect.  Suppose you're helping design an elevator.  Because of space limitations, it can hold at most 6 people at one time.  And you can be pretty sure that this will happen from time to time.  You could set the maximum weight to be something really large, like 1200 (assuming that it is unlikely that you will have 6 people with an average weight of 200 pounds all at once.) The problem is that it gets quite expensive to build an elevator that can handle a lot of weight, so you want the maximum weight to be as low as possible.  You could set the maximum weight at 200 pounds, but then lots of people would complain because you could probably never have 6 people on board, and besides people would feel nervous if the maximum weight the elevator could handle were that low.

What maximum weight would you choose for an elevator?  Suppose that each additional pound over 200 pounds costs an additional $100 in manufacturing costs, and you want to keep costs down.  Assume that the weight data taken from our class is a random sample of people and so is a good representation of the population of people who will use this elevator every day.  Use this data to choose and justify a maximum weight for this elevator. (You want it to be the smallest maximum weight you can get away with.) Explain your reasoning and state your assumptions.

How likely is your elevator to fail?  (That is, how likely is the weight limit to be exceeded.)  You can get a feel for this by using the command
(sample weight 6 t)
in ARC (type this into the "Listener" after loading the class data and naming the weight variable "weight".)  This command draws a random sample of size six without replacement from the weights.  You can add this up to simulate six people randomly getting onto the computer.  Repeat this a few times to get a feel for possible outcomes.  Of course, you'd have to do it a lot to get a good handle on the exact probability, so just do it enough to get some sort of feel for the answer.  If you just type (sample weight 6) you will get a random sample of size 6 drawn withOUT replacement.