Go to a Basketball court as a group of two or three. (Of course you can also use a different sport, like darts or throwing a ball into a trash basket, ...) Each one should try 100 free shots. Write down the results (not only the total score for each player, but also the sequence of successes and failures. The sequence of these numbers should also appear in the paper)
Next analyse the data for each player. Check whether the sequence of these throws obeys the conditions of a Bernoulli trial (only two possible outcomes, independence (or would success in one throw affect the next throw?), and that the probability of success for each player remains constant during the sequence (or would it increase, due to the practice, or would it decrease due to getting tired?)). Now compute mean and standard deviation for each player.
How likely is it for each player to obtain 70 successes in a sequence of 100? For what odds (say 10:1) would you bet on this?
How likely is it that the weakest player in the group beats the best in a 100 throw competition? How likely is it that this weakest player beats the best in a 5-throw competition? With what odds would you bet on the weaker one?
creating data, descriptive statistics, Bernoulli and normal distribution, mean estimation, probability
Erich Prisner, May 2006