Normal distribution and choosing final number

Question

I've read a paper which used normal distribution in order to assign a number to each entity as follows:

Each user has a quality measurement qi ∈ [0, 1]. For the experiments in this paper, the quality of a user is chosen from a normal distribution with 0.5 for mean and 0.5 for SD

May you please help me, what exactly they are saying?

Answer 1

Each user gets a "quality" value between 0 and 1. The probability of getting a number is symmetric about $0.5$, and is given by a normal distribution, which defines the probability of being a given "distance" away from the mean.

That "distance" is measured in standard deviations and called the $z$-value. The formula for the $z$-value of a given measurement $x$ is $$z=\frac{x-\mu}{\sigma}$$

where $\mu$ is the mean, $\sigma$ is the standard deviation.

The standard normal distribution has $\mu=0,\sigma=1$. The above formula effectively converts values on another normal distribution to the equivalent value on the standard normal distribution. The equivalence for the statement you refer to, is explained in the diagram below. Values outside the valid zone for $q_i$ are likely ignored.

Answer 2

The normal distribution is a "bell shaped curve", that appears often when the variable you are measuring is a result of multiple effect which act more-or-less independently of each other.

In a normal distribution more people will be clustered around the average, with a few above and below average. Also about 50% will be above average and 50% below average (the normal distribution is symmetric, not skewed). The normal distribution is described by two values: the mean and the variance (or the square of the standard deviation)

Distributions that approximate normal include: the heights of men chosen at random. the marks achieved in a test paper and, The amount of error made in a scientific measurement. You can generate normally distributed values in Excel with the formula =norminv(rand(),0.5,0.5)

There is an inconsistency in the example, as if qi is distributed normally, then its values could be bigger than 1 or less than 0. Perhaps another part of the paper describes how this fits with the claim that each qi is between 0 and 1.