Question

Take a guess: if 1000 balls are dropped from the top, how will they be distributed in those slots in the bottom? Are they going to be distributed evenly at the bottom and form a horizontal line, or unevenly and form a roof-top shape, or something else? Jot down your guesses and your rationales. Go back to finish the video. 1. Share your initial guesses and final observations here. 2. If you agree it is a binomial distribution, what is the parameter n, and pi, in this case? (Hint: n is NOT the number of balls dropped.)

Answer 1

Solution:

If 1000 balls are dropped and allowed to reach slots in the bottom. Each ball, as it falls, will fall either left or right, So pl = 1- pr. In other words, the probability of a ball going left (pl) is 1 minus the probability of a ball going right (pr). If the slots are symmetrically arranged, pl = pr = ½.

ball will randomly ‘choose’ one of two directions—left or right—to go around it. Eventually, each ball will fall into one of the slots at the bottom.

The balls will attain shape like normal distribution curve, which is close to roof top shape.

As the central limit theorem tells us that the sum of k random variables approaches a normal distribution as k increases, we can expect that the distribution in our slots will be normal.

Since n is small binomial distribution can also be used. This distribution will grow closer and closer to normal thelarger the number of balls that are dropped.

n= number of slots in the bottom

pi= 0.5