Question

Another type of distribution is the normal curve or sometimes called the bell curve. If a distribution has a normal curve, it is symmetrical with most of the probabilities located near the mean. Many test scores are based on a bell curve. An example of a bell curve is population IQ. The mean of the population is 100 with a standard deviation of 15.

For this week's discussion, do a little research and share another real life example of a bell-shaped data distribution or data that is normally distributed. Post a diagram to share with the class.         

Answer 1

now have you seen this game?

A quincunx or "Galton Board" (named after Sir Francis Galton) is a triangular array of pegs (have a play with it).

Balls are dropped onto the top peg and then bounce their way down to the bottom where they are collected in little bins.

Each time a ball hits one of the pegs, it bounces either left or right.

But this is interesting: when there is an equal chance of bouncing left or right, then the balls collected in the bins form the classic "bell-shaped" curve of the normal distribution.

(When the probabilities are not even, we get a nice "skewed" version of the normal distribution.)

Formula
Think about this: a ball ends up in the bin k places from the rightwhen it has taken k leftturns.

In this example, all the bounces are to the right except for two bounces to the left. It ended up in the bin two places from the right.

In the general case, when the quincunx has n rows then the ball can have k bounces to the left and (n-k)bounces to the right.

The probability is usually 50% either way, but it could be 60%-40% etc.

So when the probability of bouncing to the left is p the probability to the right is (1-p) and we can calculate the probability of any one path like this:

 The ball bounces k times to the left with a probability of p: p^k And the other bounces (n-k) have the opposite probability of: (1-p)^(n-k) So, the probability of following such a path is p^k(1-p)^(n-k)

But there could be many such paths! For example the left turns could be the 1st and 2nd, or 1st and 3rd, or 2nd and 7th, etc.

The ultimate formula then is..

now see this figure.

cleary it will form a bell shaped curve.

Clearly the game of Quincunx follows a normal distribution.

We can interpret this in the following picture.

This in one of the real life examples of a set of data that is normally distributed.

(Kindly note that the resources have been followed and obtained from internet. I don't own the information provided here.)